cons_logicor.c

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/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
/*                                                                           */
/*                  This file is part of the program and library             */
/*         SCIP --- Solving Constraint Integer Programs                      */
/*                                                                           */
/*    Copyright (C) 2002-2015 Konrad-Zuse-Zentrum                            */
/*                            fuer Informationstechnik Berlin                */
/*                                                                           */
/*  SCIP is distributed under the terms of the ZIB Academic License.         */
/*                                                                           */
/*  You should have received a copy of the ZIB Academic License              */
/*  along with SCIP; see the file COPYING. If not email to scip@zib.de.      */
/*                                                                           */
/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */

/**@file   cons_logicor.c
 * @brief  Constraint handler for logic or constraints \f$1^T x \ge 1\f$
 *         (equivalent to set covering, but algorithms are suited for depth first search).
 * @author Tobias Achterberg
 * @author Michael Winkler
 */

/*---+----1----+----2----+----3----+----4----+----5----+----6----+----7----+----8----+----9----+----0----+----1----+----2*/

#include <assert.h>
#include <string.h>
#include <limits.h>

#include "scip/cons_logicor.h"
#include "scip/cons_linear.h"
#include "scip/cons_setppc.h"
#include "scip/pub_misc.h"


#define CONSHDLR_NAME          "logicor"
#define CONSHDLR_DESC          "logic or constraints"
#define CONSHDLR_SEPAPRIORITY    +10000 /**< priority of the constraint handler for separation */
#define CONSHDLR_ENFOPRIORITY  -2000000 /**< priority of the constraint handler for constraint enforcing */
#define CONSHDLR_CHECKPRIORITY -2000000 /**< priority of the constraint handler for checking feasibility */
#define CONSHDLR_SEPAFREQ             0 /**< frequency for separating cuts; zero means to separate only in the root node */
#define CONSHDLR_PROPFREQ             1 /**< frequency for propagating domains; zero means only preprocessing propagation */
#define CONSHDLR_EAGERFREQ          100 /**< frequency for using all instead of only the useful constraints in separation,
                                         *   propagation and enforcement, -1 for no eager evaluations, 0 for first only */
#define CONSHDLR_MAXPREROUNDS        -1 /**< maximal number of presolving rounds the constraint handler participates in (-1: no limit) */
#define CONSHDLR_DELAYSEPA        FALSE /**< should separation method be delayed, if other separators found cuts? */
#define CONSHDLR_DELAYPROP        FALSE /**< should propagation method be delayed, if other propagators found reductions? */
#define CONSHDLR_NEEDSCONS         TRUE /**< should the constraint handler be skipped, if no constraints are available? */

#define CONSHDLR_PRESOLTIMING            SCIP_PRESOLTIMING_ALWAYS
#define CONSHDLR_PROP_TIMING             SCIP_PROPTIMING_BEFORELP

#define LINCONSUPGD_PRIORITY    +800000 /**< priority of the constraint handler for upgrading of linear constraints */

#define EVENTHDLR_NAME         "logicor"
#define EVENTHDLR_DESC         "event handler for logic or constraints"

#define CONFLICTHDLR_NAME      "logicor"
#define CONFLICTHDLR_DESC      "conflict handler creating logic or constraints"
#define CONFLICTHDLR_PRIORITY  LINCONSUPGD_PRIORITY

#define DEFAULT_PRESOLPAIRWISE     TRUE /**< should pairwise constraint comparison be performed in presolving? */
#define DEFAULT_STRENGTHEN         TRUE /**< should pairwise constraint comparison try to strengthen constraints by removing superflous non-zeros? */

#define HASHSIZE_LOGICORCONS     131101 /**< minimal size of hash table in logicor constraint tables */
#define DEFAULT_PRESOLUSEHASHING   TRUE /**< should hash table be used for detecting redundant constraints in advance */
#define DEFAULT_DUALPRESOLVING     TRUE /**< should dual presolving steps be performed? */
#define DEFAULT_NEGATEDCLIQUE      TRUE /**< should negated clique information be used in presolving */
#define DEFAULT_IMPLICATIONS       TRUE /**< should we try to shrink the variables and derive global boundchanges by
                                         *   using cliques and implications */

/* @todo make this a parameter setting */
#if 1 /* @todo test which AGEINCREASE formula is better! */
#define AGEINCREASE(n) (1.0 + 0.2 * (n))
#else
#define AGEINCREASE(n) (0.1 * (n))
#endif


/* @todo maybe use event SCIP_EVENTTYPE_VARUNLOCKED to decide for another dual-presolving run on a constraint */

/*
 * Data structures
 */

/** constraint handler data */
struct SCIP_ConshdlrData
{
   SCIP_EVENTHDLR*       eventhdlr;          /**< event handler for events on watched variables */
   SCIP_CONSHDLR*        conshdlrlinear;     /**< pointer to linear constraint handler or NULL if not included */
   SCIP_CONSHDLR*        conshdlrsetppc;     /**< pointer to setppc constraint handler or NULL if not included */
   SCIP_Bool             presolpairwise;     /**< should pairwise constraint comparison be performed in presolving? */
   SCIP_Bool             presolusehashing;   /**< should hash table be used for detecting redundant constraints in
                                              *   advance */
   SCIP_Bool             dualpresolving;     /**< should dual presolving steps be performed? */
   SCIP_Bool             usenegatedclique;   /**< should negated clique information be used in presolving */
   SCIP_Bool             useimplications;    /**< should we try to shrink the variables and derive global boundchanges
                                              *   by using clique and implications */
   SCIP_Bool             usestrengthening;   /**< should pairwise constraint comparison try to strengthen constraints by
                                              *   removing superflous non-zeros? */
   int                   nlastcliquesneg;    /**< number of cliques after last negated clique presolving round */
   int                   nlastimplsneg;      /**< number of implications after last negated clique presolving round */
   int                   nlastcliquesshorten;/**< number of cliques after last shortening of constraints */
   int                   nlastimplsshorten;  /**< number of implications after last shortening of constraints */
};

/* @todo it might speed up exit-presolve to remember all positions for variables when catching the varfixed event, or we
 *       change catching and dropping the events like it is done in cons_setppc, which probably makes the code more
 *       clear
 */

/** logic or constraint data */
struct SCIP_ConsData
{
   SCIP_ROW*             row;                /**< LP row, if constraint is already stored in LP row format */
   SCIP_VAR**            vars;               /**< variables of the constraint */
   int                   varssize;           /**< size of vars array */
   int                   nvars;              /**< number of variables in the constraint */
   int                   watchedvar1;        /**< position of the first watched variable */
   int                   watchedvar2;        /**< position of the second watched variable */
   int                   filterpos1;         /**< event filter position of first watched variable */
   int                   filterpos2;         /**< event filter position of second watched variable */
   unsigned int          signature;          /**< constraint signature which is need for pairwise comparison */
   unsigned int          presolved:1;        /**< flag indicates if we have some fixed, aggregated or multi-aggregated
                                              *   variables
                                              */
   unsigned int          impladded:1;        /**< was the 2-variable logic or constraint already added as implication? */
   unsigned int          sorted:1;           /**< are the constraint's variables sorted? */
   unsigned int          changed:1;          /**< was constraint changed since last redundancy round in preprocessing? */
   unsigned int          merged:1;           /**< are the constraint's equal/negated variables already merged? */
   unsigned int          existmultaggr:1;    /**< does this constraint contain aggregations */
   unsigned int          validsignature:1;   /**< is the signature valid */

};


/*
 * Local methods
 */

/** installs rounding locks for the given variable in the given logic or constraint */
static
SCIP_RETCODE lockRounding(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_VAR*             var                 /**< variable of constraint entry */
   )
{
   /* rounding down may violate the constraint */
   SCIP_CALL( SCIPlockVarCons(scip, var, cons, TRUE, FALSE) );

   return SCIP_OKAY;
}

/** removes rounding locks for the given variable in the given logic or constraint */
static
SCIP_RETCODE unlockRounding(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_VAR*             var                 /**< variable of constraint entry */
   )
{
   /* rounding down may violate the constraint */
   SCIP_CALL( SCIPunlockVarCons(scip, var, cons, TRUE, FALSE) );

   return SCIP_OKAY;
}

/** creates constraint handler data for logic or constraint handler */
static
SCIP_RETCODE conshdlrdataCreate(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLRDATA**   conshdlrdata,       /**< pointer to store the constraint handler data */
   SCIP_EVENTHDLR*       eventhdlr           /**< event handler */
   )
{
   assert(scip != NULL);
   assert(conshdlrdata != NULL);
   assert(eventhdlr != NULL);

   SCIP_CALL( SCIPallocMemory(scip, conshdlrdata) );

   (*conshdlrdata)->nlastcliquesneg = 0;
   (*conshdlrdata)->nlastimplsneg = 0;
   (*conshdlrdata)->nlastcliquesshorten = 0;
   (*conshdlrdata)->nlastimplsshorten = 0;

   /* set event handler for catching events on watched variables */
   (*conshdlrdata)->eventhdlr = eventhdlr;

   return SCIP_OKAY;
}

/** frees constraint handler data for logic or constraint handler */
static
SCIP_RETCODE conshdlrdataFree(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLRDATA**   conshdlrdata        /**< pointer to the constraint handler data */
   )
{
   assert(conshdlrdata != NULL);
   assert(*conshdlrdata != NULL);

   SCIPfreeMemory(scip, conshdlrdata);

   return SCIP_OKAY;
}

/** ensures, that the vars array can store at least num entries */
static
SCIP_RETCODE consdataEnsureVarsSize(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< logicor constraint data */
   int                   num                 /**< minimum number of entries to store */
   )
{
   assert(consdata != NULL);
   assert(consdata->nvars <= consdata->varssize);

   if( num > consdata->varssize )
   {
      int newsize;

      newsize = SCIPcalcMemGrowSize(scip, num);
      SCIP_CALL( SCIPreallocBlockMemoryArray(scip, &consdata->vars, consdata->varssize, newsize) );
      consdata->varssize = newsize;
   }
   assert(num <= consdata->varssize);

   return SCIP_OKAY;
}

/** creates a logic or constraint data object */
static
SCIP_RETCODE consdataCreate(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA**       consdata,           /**< pointer to store the logic or constraint data */
   int                   nvars,              /**< number of variables in the constraint */
   SCIP_VAR**            vars                /**< variables of the constraint */
   )
{
   int v;

   assert(consdata != NULL);
   assert(nvars == 0 || vars != NULL);

   SCIP_CALL( SCIPallocBlockMemory(scip, consdata) );

   (*consdata)->row = NULL;
   if( nvars > 0 )
   {
      SCIP_CALL( SCIPduplicateBlockMemoryArray(scip, &(*consdata)->vars, vars, nvars) );
      (*consdata)->varssize = nvars;
      (*consdata)->nvars = nvars;
   }
   else
   {
      (*consdata)->vars = NULL;
      (*consdata)->varssize = 0;
      (*consdata)->nvars = 0;
   }
   (*consdata)->watchedvar1 = -1;
   (*consdata)->watchedvar2 = -1;
   (*consdata)->filterpos1 = -1;
   (*consdata)->filterpos2 = -1;
   (*consdata)->presolved = FALSE;
   (*consdata)->impladded = FALSE;
   (*consdata)->changed = TRUE;
   (*consdata)->sorted = (nvars <= 1);
   (*consdata)->merged = (nvars <= 1);
   (*consdata)->existmultaggr = FALSE;
   (*consdata)->validsignature = FALSE;

   /* get transformed variables, if we are in the transformed problem */
   if( SCIPisTransformed(scip) )
   {
      SCIP_CALL( SCIPgetTransformedVars(scip, (*consdata)->nvars, (*consdata)->vars, (*consdata)->vars) );

      /* check for multi-aggregations and capture variables */
      for( v = 0; v < (*consdata)->nvars; v++ )
      {
         SCIP_VAR* var = SCIPvarGetProbvar((*consdata)->vars[v]);
         assert(var != NULL);
         (*consdata)->existmultaggr = (*consdata)->existmultaggr || (SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR);
         SCIP_CALL( SCIPcaptureVar(scip, (*consdata)->vars[v]) );
      }
   }
   else
   {
      /* capture variables */
      for( v = 0; v < (*consdata)->nvars; v++ )
      {
         assert((*consdata)->vars[v] != NULL);
         SCIP_CALL( SCIPcaptureVar(scip, (*consdata)->vars[v]) );
      }
   }

   return SCIP_OKAY;
}

/** frees a logic or constraint data */
static
SCIP_RETCODE consdataFree(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA**       consdata            /**< pointer to the logic or constraint */
   )
{
   int v;

   assert(consdata != NULL);
   assert(*consdata != NULL);

   /* release the row */
   if( (*consdata)->row != NULL )
   {
      SCIP_CALL( SCIPreleaseRow(scip, &(*consdata)->row) );
   }

   /* release variables */
   for( v = 0; v < (*consdata)->nvars; v++ )
   {
      assert((*consdata)->vars[v] != NULL);
      SCIP_CALL( SCIPreleaseVar(scip, &((*consdata)->vars[v])) );
   }

   SCIPfreeBlockMemoryArrayNull(scip, &(*consdata)->vars, (*consdata)->varssize);
   SCIPfreeBlockMemory(scip, consdata);

   return SCIP_OKAY;
}

/** prints logic or constraint to file stream */
static
SCIP_RETCODE consdataPrint(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSDATA*        consdata,           /**< logic or constraint data */
   FILE*                 file,               /**< output file (or NULL for standard output) */
   SCIP_Bool             endline             /**< should an endline be set? */
   )
{
   assert(consdata != NULL);

   /* print constraint type */
   SCIPinfoMessage(scip, file, "logicor(");

   /* print variable list */
   SCIP_CALL( SCIPwriteVarsList(scip, file, consdata->vars, consdata->nvars, TRUE, ',') );

   /* close bracket */
   SCIPinfoMessage(scip, file, ")");

   if( endline )
      SCIPinfoMessage(scip, file, "\n");

   return SCIP_OKAY;
}

/** stores the given variable numbers as watched variables, and updates the event processing */
static
SCIP_RETCODE switchWatchedvars(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   int                   watchedvar1,        /**< new first watched variable */
   int                   watchedvar2         /**< new second watched variable */
   )
{
   SCIP_CONSDATA* consdata;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(watchedvar1 == -1 || watchedvar1 != watchedvar2);
   assert(watchedvar1 != -1 || watchedvar2 == -1);
   assert(watchedvar1 == -1 || (0 <= watchedvar1 && watchedvar1 < consdata->nvars));
   assert(watchedvar2 == -1 || (0 <= watchedvar2 && watchedvar2 < consdata->nvars));

   /* if one watched variable is equal to the old other watched variable, just switch positions */
   if( watchedvar1 == consdata->watchedvar2 || watchedvar2 == consdata->watchedvar1 )
   {
      int tmp;

      tmp = consdata->watchedvar1;
      consdata->watchedvar1 = consdata->watchedvar2;
      consdata->watchedvar2 = tmp;
      tmp = consdata->filterpos1;
      consdata->filterpos1 = consdata->filterpos2;
      consdata->filterpos2 = tmp;
   }
   assert(watchedvar1 == -1 || watchedvar1 != consdata->watchedvar2);
   assert(watchedvar2 == -1 || watchedvar2 != consdata->watchedvar1);

   /* drop events on old watched variables */
   if( consdata->watchedvar1 != -1 && consdata->watchedvar1 != watchedvar1 )
   {
      assert(consdata->filterpos1 != -1);
      SCIP_CALL( SCIPdropVarEvent(scip, consdata->vars[consdata->watchedvar1],
            SCIP_EVENTTYPE_UBTIGHTENED | SCIP_EVENTTYPE_LBRELAXED, eventhdlr, (SCIP_EVENTDATA*)cons,
            consdata->filterpos1) );
   }
   if( consdata->watchedvar2 != -1 && consdata->watchedvar2 != watchedvar2 )
   {
      assert(consdata->filterpos2 != -1);
      SCIP_CALL( SCIPdropVarEvent(scip, consdata->vars[consdata->watchedvar2],
            SCIP_EVENTTYPE_UBTIGHTENED | SCIP_EVENTTYPE_LBRELAXED, eventhdlr, (SCIP_EVENTDATA*)cons, 
            consdata->filterpos2) );
   }

   /* catch events on new watched variables */
   if( watchedvar1 != -1 && watchedvar1 != consdata->watchedvar1 )
   {
      SCIP_CALL( SCIPcatchVarEvent(scip, consdata->vars[watchedvar1],
            SCIP_EVENTTYPE_UBTIGHTENED | SCIP_EVENTTYPE_LBRELAXED, eventhdlr, (SCIP_EVENTDATA*)cons,
            &consdata->filterpos1) );
   }
   if( watchedvar2 != -1 && watchedvar2 != consdata->watchedvar2 )
   {
      SCIP_CALL( SCIPcatchVarEvent(scip, consdata->vars[watchedvar2],
            SCIP_EVENTTYPE_UBTIGHTENED | SCIP_EVENTTYPE_LBRELAXED, eventhdlr, (SCIP_EVENTDATA*)cons,
            &consdata->filterpos2) );
   }

   /* set the new watched variables */
   consdata->watchedvar1 = watchedvar1;
   consdata->watchedvar2 = watchedvar2;

   return SCIP_OKAY;
}

/** adds coefficient in logicor constraint */
static
SCIP_RETCODE addCoef(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logicor constraint */
   SCIP_VAR*             var                 /**< variable to add to the constraint */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Bool transformed;

   assert(var != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* are we in the transformed problem? */
   transformed = SCIPconsIsTransformed(cons);

   /* always use transformed variables in transformed constraints */
   if( transformed )
   {
      SCIP_CALL( SCIPgetTransformedVar(scip, var, &var) );

      if( !consdata->existmultaggr && SCIPvarGetStatus(SCIPvarGetProbvar(var)) == SCIP_VARSTATUS_MULTAGGR )
         consdata->existmultaggr = TRUE;

      consdata->presolved = FALSE;
   }
   assert(var != NULL);
   assert(transformed == SCIPvarIsTransformed(var));

   SCIP_CALL( consdataEnsureVarsSize(scip, consdata, consdata->nvars + 1) );
   consdata->vars[consdata->nvars] = var;
   SCIP_CALL( SCIPcaptureVar(scip, consdata->vars[consdata->nvars]) );
   consdata->nvars++;

   /* we only catch this event in presolving stage */
   if( SCIPgetStage(scip) == SCIP_STAGE_PRESOLVING || SCIPgetStage(scip) == SCIP_STAGE_INITPRESOLVE )
   {
      SCIP_CONSHDLRDATA* conshdlrdata;
      SCIP_CONSHDLR* conshdlr;

      conshdlr = SCIPfindConshdlr(scip, CONSHDLR_NAME);
      assert(conshdlr != NULL);
      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);

      SCIP_CALL( SCIPcatchVarEvent(scip, var, SCIP_EVENTTYPE_VARFIXED, conshdlrdata->eventhdlr,
            (SCIP_EVENTDATA*)cons, NULL) );
   }

   consdata->sorted = (consdata->nvars == 1);
   consdata->changed = TRUE;
   consdata->validsignature = FALSE;

   /* install the rounding locks for the new variable */
   SCIP_CALL( lockRounding(scip, cons, var) );

   /* add the new coefficient to the LP row */
   if( consdata->row != NULL )
   {
      SCIP_CALL( SCIPaddVarToRow(scip, consdata->row, var, 1.0) );
   }

   consdata->merged = FALSE;

   return SCIP_OKAY;
}

/** deletes coefficient at given position from logic or constraint data */
static
SCIP_RETCODE delCoefPos(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   int                   pos                 /**< position of coefficient to delete */
   )
{
   SCIP_CONSDATA* consdata;

   assert(eventhdlr != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(0 <= pos && pos < consdata->nvars);
   assert(SCIPconsIsTransformed(cons) == SCIPvarIsTransformed(consdata->vars[pos]));

   /* remove the rounding locks of variable */
   SCIP_CALL( unlockRounding(scip, cons, consdata->vars[pos]) );

   /* we only catch this event in presolving stage, so we need to only drop it there */
   if( SCIPgetStage(scip) == SCIP_STAGE_PRESOLVING || SCIPgetStage(scip) == SCIP_STAGE_INITPRESOLVE )
   {
      SCIP_CALL( SCIPdropVarEvent(scip, consdata->vars[pos], SCIP_EVENTTYPE_VARFIXED, eventhdlr,
            (SCIP_EVENTDATA*)cons, -1) );
   }

   if( SCIPconsIsTransformed(cons) )
   {
      /* if the position is watched, stop watching the position */
      if( consdata->watchedvar1 == pos )
      {
         SCIP_CALL( switchWatchedvars(scip, cons, eventhdlr, consdata->watchedvar2, -1) );
      }
      if( consdata->watchedvar2 == pos )
      {
         SCIP_CALL( switchWatchedvars(scip, cons, eventhdlr, consdata->watchedvar1, -1) );
      }
   }
   assert(pos != consdata->watchedvar1);
   assert(pos != consdata->watchedvar2);

   /* release variable */
   SCIP_CALL( SCIPreleaseVar(scip, &consdata->vars[pos]) );

   /* move the last variable to the free slot */
   if( pos != consdata->nvars - 1 )
   {
      consdata->vars[pos] = consdata->vars[consdata->nvars-1];
      consdata->sorted = FALSE;
   }
   consdata->nvars--;

   /* if the last variable (that moved) was watched, update the watched position */
   if( consdata->watchedvar1 == consdata->nvars )
      consdata->watchedvar1 = pos;
   if( consdata->watchedvar2 == consdata->nvars )
      consdata->watchedvar2 = pos;

   consdata->changed = TRUE;
   consdata->validsignature = FALSE;

   SCIP_CALL( SCIPenableConsPropagation(scip, cons) );

   return SCIP_OKAY;
}

/** in case a part (more than one variable) in the logic or constraint is independent of every else, we can perform dual
 *  reductions;
 *  - fix the variable with the smallest object coefficient to one if the constraint is not modifiable and all
 *    variable are independant
 *  - fix all independant variables with negative object coefficient to one
 *  - fix all remaining independant variables to zero
 *
 *  also added the special case were exactly one variable is locked by this constraint and another variable without any
 *  uplocks has a better objective value than this single variable
 *  - here we fix the variable to 0.0 (if the objective contribution is non-negative)
 *
 * Note: the following dual reduction for logic or constraints is already performed by the presolver "dualfix"
 *       - if a variable in a set covering constraint is only locked by that constraint and has negative or zero
 *         objective coefficient than it can be fixed to one
 */
static
SCIP_RETCODE dualPresolving(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< setppc constraint */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   int*                  nfixedvars,         /**< pointer to count number of fixings */
   int*                  ndelconss,          /**< pointer to count number of deleted constraints  */
   int*                  nchgcoefs,          /**< pointer to count number of changed/deleted coefficients */
   SCIP_RESULT*          result              /**< pointer to store the result SCIP_SUCCESS, if presolving was performed */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR** vars;
   SCIP_VAR* var;
   SCIP_VAR* activevar;
   SCIP_Real bestobjval;
   SCIP_Real bestobjvalnouplocks;
   SCIP_Real objval;
   SCIP_Real fixval;
   SCIP_Bool infeasible;
   SCIP_Bool fixed;
   SCIP_Bool negated;
   int nfixables;
   int nvars;
   int idx;
   int idxnouplocks;
   int v;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(eventhdlr != NULL);
   assert(nfixedvars != NULL);
   assert(ndelconss != NULL);
   assert(nchgcoefs != NULL);
   assert(result != NULL);

   /* constraints for which the check flag is set to FALSE, did not contribute to the lock numbers; therefore, we cannot
    * use the locks to decide for a dual reduction using this constraint; for example after a restart the cuts which are
    * added to the problems have the check flag set to FALSE 
    */
   if( !SCIPconsIsChecked(cons) )
      return SCIP_OKAY;

   assert(SCIPconsIsActive(cons));

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   nvars = consdata->nvars;

   /* we don't want to consider small constraints (note that the constraints can be modifiable, so we can't delete this
    * constraint)
    */
   if( nvars < 2 )
      return SCIP_OKAY;

   vars = consdata->vars;
   idx = -1;
   idxnouplocks = -1;
   bestobjval = SCIP_INVALID;
   bestobjvalnouplocks = SCIP_INVALID;

   nfixables = 0;

   /* check if we can apply the dual reduction; therefore count the number of variables where the logic or has the only
    * locks on
    */
   for( v = nvars - 1; v >= 0; --v )
   {
      var = vars[v];
      assert(var != NULL);

      /* variables with varstatus not equal to SCIP_VARSTATUS_FIXED can also have fixed bounds, but were not removed yet */
      if( SCIPvarGetUbGlobal(var) < 0.5 )
      {
#ifndef NDEBUG
         SCIP_VAR* bestvar = NULL;
#endif
         if( idx == consdata->nvars - 1 )
         {
#ifndef NDEBUG
            bestvar = consdata->vars[idx];
#endif
            idx = v;
         }

         SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );
         ++(*nchgcoefs);

         assert(bestvar == NULL || bestvar == consdata->vars[v]);

         continue;
      }
      if( SCIPvarGetLbGlobal(var) > 0.5 )
      {
         /* remove constraint since it is redundant */
         SCIP_CALL( SCIPdelCons(scip, cons) );
         ++(*ndelconss);

         return SCIP_OKAY;
      }

      /* remember best variable with no uplocks, this variable dominates all other with exactly one downlock */
      if( SCIPvarGetNLocksDown(var) > 1 && SCIPvarGetNLocksUp(var) == 0 )
      {
         SCIP_CALL( SCIPvarGetAggregatedObj(var, &objval) );

         /* check if the current variable has a smaller objective coefficient then the best one */
         if( SCIPisLT(scip, objval, bestobjval) )
         {
            idxnouplocks = v;
            bestobjvalnouplocks = objval;
         }
      }

      /* in case an other constraints has also locks on that variable we cannot perform a dual reduction on these
       * variables
       */
      if( SCIPvarGetNLocksDown(var) > 1 || SCIPvarGetNLocksUp(var) > 0 )
         continue;

      ++nfixables;
      negated = FALSE;

      /* get the active variable */
      SCIP_CALL( SCIPvarGetProbvarBinary(&var, &negated) );
      assert(SCIPvarIsActive(var));

      if( negated )
         objval = -SCIPvarGetObj(var);
      else
         objval = SCIPvarGetObj(var);

      /* check if the current variable has a smaller objective coefficient */
      if( SCIPisLT(scip, objval, bestobjval) )
      {
         idx = v;
         bestobjval = objval;
      }
   }

   nvars = consdata->nvars;

   /* check if we have a single variable dominated by another */
   if( nfixables == 1 && idxnouplocks >= 0 )
   {
      assert(bestobjvalnouplocks != SCIP_INVALID); /*lint !e777*/

      for( v = nvars - 1; v >= 0; --v )
      {
         var = vars[v];
         assert(var != NULL);

         /* check if a variable only appearing in this constraint is dominated by another */
         if( SCIPvarGetNLocksDown(var) == 1 && SCIPvarGetNLocksUp(var) == 0 )
         {
            assert(idxnouplocks != v);

            SCIP_CALL( SCIPvarGetAggregatedObj(var, &objval) );

            if( SCIPisGE(scip, objval, bestobjvalnouplocks) && !SCIPisNegative(scip, objval) )
            {
               SCIP_CALL( SCIPfixVar(scip, var, 0.0, &infeasible, &fixed) );
               assert(!infeasible);
               assert(fixed);

               SCIPdebugMessage(" -> dual fixing <%s> == 0.0\n", SCIPvarGetName(var));
               ++(*nfixedvars);
            }

            break;
         }
      }
   }

   if( nfixables < 2 )
      return SCIP_OKAY;

   nvars = consdata->nvars;

   assert(idx >= 0 && idx < nvars);
   assert(bestobjval < SCIPinfinity(scip));

   *result = SCIP_SUCCESS;

   /* fix all redundant variables to their best bound */

   /* first part of all variables */
   for( v = 0; v < nvars; ++v )
   {
      var = vars[v];
      assert(var != NULL);

      /* in case an other constraints has also locks on that variable we cannot perform a dual reduction on these
       * variables
       */
      if( SCIPvarGetNLocksDown(var) > 1 || SCIPvarGetNLocksUp(var) > 0 )
         continue;

      if( v == idx )
         continue;

      activevar = var;
      negated = FALSE;

      /* get the active variable */
      SCIP_CALL( SCIPvarGetProbvarBinary(&activevar, &negated) );
      assert(SCIPvarIsActive(activevar));

      if( negated )
         objval = -SCIPvarGetObj(activevar);
      else
         objval = SCIPvarGetObj(activevar);

      if( objval > 0.0 )
         fixval = 0.0;
      else
         fixval = 1.0;

      SCIP_CALL( SCIPfixVar(scip, var, fixval, &infeasible, &fixed) );
      assert(!infeasible);
      assert(fixed);

      SCIPdebugMessage(" -> dual fixing <%s> == %g\n", SCIPvarGetName(var), fixval);
      ++(*nfixedvars);
   }

   /* if all variable have our appreciated number of locks and the constraint is not modifiable, or if the bestobjval is
    * less than or equal to zero, we can fix the variable with the smallest objective coefficient to one and the
    * constraint gets redundant
    */
   if( (nfixables == nvars && !SCIPconsIsModifiable(cons)) || bestobjval <= 0.0 )
   {
      SCIP_CALL( SCIPfixVar(scip, vars[idx], 1.0, &infeasible, &fixed) );
      assert(!infeasible);
      assert(fixed);

      SCIPdebugMessage(" -> fixed <%s> == 1.0\n", SCIPvarGetName(vars[idx]));
      ++(*nfixedvars);

      /* remove constraint since it is now redundant */
      SCIP_CALL( SCIPdelCons(scip, cons) );
      ++(*ndelconss);
   }

   return SCIP_OKAY;
}

/** deletes all zero-fixed variables, checks for variables fixed to one, replace all variables which are not active or
 *  not a negation of an active variable by there active or negation of an active counterpart
 */
static
SCIP_RETCODE applyFixings(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   SCIP_Bool*            redundant,          /**< returns whether a variable fixed to one exists in the constraint */
   int*                  nchgcoefs,          /**< pointer to count number of changed/deleted coefficients */
   int*                  naddconss,          /**< pointer to count number of added constraints, or NULL indicating we
                                              *   can not resolve multi-aggregations
                                              */
   int*                  ndelconss           /**< pointer to count number of deleted constraints, or NULL indicating we
                                              *   can not resolve multi-aggregations
                                              */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR* var;
   int v;
   SCIP_VAR** vars;
   SCIP_Bool* negarray;
   int nvars;

   assert(eventhdlr != NULL);
   assert(redundant != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->nvars == 0 || consdata->vars != NULL);

   *redundant = FALSE;
   v = 0;

   /* all multi-aggregations should be resolved */
   consdata->existmultaggr = FALSE;
   consdata->presolved = TRUE;

   /* remove zeros and mark constraint redundant when found one variable fixed to one */
   while( v < consdata->nvars )
   {
      var = consdata->vars[v];
      assert(SCIPvarIsBinary(var));

      if( SCIPvarGetLbGlobal(var) > 0.5 )
      {
         assert(SCIPisFeasEQ(scip, SCIPvarGetUbGlobal(var), 1.0));
         *redundant = TRUE;

         return SCIP_OKAY;
      }
      else if( SCIPvarGetUbGlobal(var) < 0.5 )
      {
         assert(SCIPisFeasEQ(scip, SCIPvarGetLbGlobal(var), 0.0));
         SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );
         ++(*nchgcoefs);
      }
      else
         ++v;
   }

   if( consdata->nvars == 0 )
      return SCIP_OKAY;

   nvars = consdata->nvars;

   /* allocate temporary memory */
   SCIP_CALL( SCIPallocBufferArray(scip, &vars, nvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &negarray, nvars) );

   /* get active or negation of active variables */
   SCIP_CALL( SCIPgetBinvarRepresentatives(scip, nvars, consdata->vars, vars, negarray) );

   /* renew all variables, important that we do a backwards loop because deletion only affect rear items */
   for( v = nvars - 1; v >= 0; --v )
   {
      var = vars[v];

      /* resolve multi-aggregation */
      if( SCIPvarGetStatus(var) == SCIP_VARSTATUS_MULTAGGR || (SCIPvarGetStatus(var) == SCIP_VARSTATUS_NEGATED && SCIPvarGetStatus(SCIPvarGetNegatedVar(var)) == SCIP_VARSTATUS_MULTAGGR) )
      {
         SCIP_VAR** consvars;
         SCIP_Real* consvals;
         SCIP_Real constant = 0.0;
         SCIP_Bool easycase;
         int nconsvars;
         int requiredsize;
         int v2;

         nconsvars = 1;
         SCIP_CALL( SCIPallocBufferArray(scip, &consvars, 1) );
         SCIP_CALL( SCIPallocBufferArray(scip, &consvals, 1) );
         consvars[0] = var;
         consvals[0] = 1.0;

         /* get active variables for new constraint */
         SCIP_CALL( SCIPgetProbvarLinearSum(scip, consvars, consvals, &nconsvars, nconsvars, &constant, &requiredsize, TRUE) );
         /* if space was not enough we need to resize the buffers */
         if( requiredsize > nconsvars )
         {
            SCIP_CALL( SCIPreallocBufferArray(scip, &consvars, requiredsize) );
            SCIP_CALL( SCIPreallocBufferArray(scip, &consvals, requiredsize) );

            SCIP_CALL( SCIPgetProbvarLinearSum(scip, consvars, consvals, &nconsvars, requiredsize, &constant, &requiredsize, TRUE) );
            assert(requiredsize <= nconsvars);
         }

         easycase = FALSE;

         if( SCIPisZero(scip, constant) )
         {
            /* add active representation */
            for( v2 = nconsvars - 1; v2 >= 0; --v2 )
            {
               if( !SCIPvarIsBinary(consvars[v2]) )
               {
                  break;
#if 0
                  SCIPerrorMessage("try to resolve a multi-aggregation with a non-binary variable <%s>\n", consvars[v2]);
                  return SCIP_ERROR;
#endif
               }

               if( !SCIPisEQ(scip, consvals[v2], 1.0) )
                  break;
            }

            if( v2 < 0 )
               easycase = TRUE;
         }

         /* we can easily add the coefficients and still have a logicor constraint */
         if( easycase )
         {
            /* delete old (multi-aggregated) variable */
            SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );
            ++(*nchgcoefs);

            /* add active representation */
            for( v2 = nconsvars - 1; v2 >= 0; --v2 )
            {
               assert(SCIPvarIsBinary(consvars[v2]));
               assert(SCIPvarIsActive(consvars[v2]) || (SCIPvarGetStatus(consvars[v2]) == SCIP_VARSTATUS_NEGATED && SCIPvarIsActive(SCIPvarGetNegationVar(consvars[v2]))));

               SCIP_CALL( addCoef(scip, cons, consvars[v2]) );
               ++(*nchgcoefs);
            }
         }
         /* we need to degrade this logicor constraint to a linear constraint*/
         else if( (ndelconss != NULL && naddconss != NULL) || SCIPconsIsAdded(cons) )
         {
            char name[SCIP_MAXSTRLEN];
            SCIP_CONS* newcons;
            SCIP_Real lhs;
            SCIP_Real rhs;
            int size;
            int k;

            /* it might happen that there are more than one multi-aggregated variable, so we need to get the whole probvar sum over all variables */

            size = MAX(nconsvars, 1) + nvars - 1;

            /* memory needed is at least old number of variables - 1 + number of variables in first multi-aggregation */
            SCIP_CALL( SCIPreallocBufferArray(scip, &consvars, size) );
            SCIP_CALL( SCIPreallocBufferArray(scip, &consvals, size) );

            nconsvars = nvars;

            /* add constraint variables to new linear variables */
            for( k = nvars - 1; k >= 0; --k )
            {
               consvars[k] = vars[k];
               consvals[k] = 1.0;
            }

            constant = 0.0;

            /* get active variables for new constraint */
            SCIP_CALL( SCIPgetProbvarLinearSum(scip, consvars, consvals, &nconsvars, size, &constant, &requiredsize, TRUE) );

            /* if space was not enough(we found another multi-aggregation), we need to resize the buffers */
            if( requiredsize > nconsvars )
            {
               SCIP_CALL( SCIPreallocBufferArray(scip, &consvars, requiredsize) );
               SCIP_CALL( SCIPreallocBufferArray(scip, &consvals, requiredsize) );

               SCIP_CALL( SCIPgetProbvarLinearSum(scip, consvars, consvals, &nconsvars, requiredsize, &constant, &requiredsize, TRUE) );
               assert(requiredsize <= nconsvars);
            }

            lhs = 1.0 - constant;
            rhs = SCIPinfinity(scip);

            /* create linear constraint */
            (void)SCIPsnprintf(name, SCIP_MAXSTRLEN, "%s", SCIPconsGetName(cons));
            SCIP_CALL( SCIPcreateConsLinear(scip, &newcons, name, nconsvars, consvars, consvals, lhs, rhs,
                  SCIPconsIsInitial(cons),
                  SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), SCIPconsIsChecked(cons),
                  SCIPconsIsPropagated(cons),  SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
                  SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
            SCIP_CALL( SCIPaddCons(scip, newcons) );

            SCIPdebugMessage("added linear constraint: ");
            SCIPdebugPrintCons(scip, newcons, NULL);
            SCIP_CALL( SCIPreleaseCons(scip, &newcons) );

            SCIPfreeBufferArray(scip, &consvals);
            SCIPfreeBufferArray(scip, &consvars);

            /* delete old constraint */
            SCIP_CALL( SCIPdelCons(scip, cons) );
            if( ndelconss != NULL && naddconss != NULL )
            {
               ++(*ndelconss);
               ++(*naddconss);
            }

            goto TERMINATE;
         }
         /* we need to degrade this logicor constraint to a linear constraint*/
         else
         {
            if( var != consdata->vars[v] )
            {
               SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );
               SCIP_CALL( addCoef(scip, cons, var) );
            }

            SCIPwarningMessage(scip, "logicor constraint <%s> has a multi-aggregated variable, which was not resolved and therefore could lead to aborts\n", SCIPconsGetName(cons));
         }

         SCIPfreeBufferArray(scip, &consvals);
         SCIPfreeBufferArray(scip, &consvars);
      }
      else if( var != consdata->vars[v] )
      {
         SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );
         SCIP_CALL( addCoef(scip, cons, var) );
      }
   }

   SCIPdebugMessage("after fixings: ");
   SCIPdebug( SCIP_CALL(consdataPrint(scip, consdata, NULL, TRUE)) );

 TERMINATE:
   /* free temporary memory */
   SCIPfreeBufferArray(scip, &negarray);
   SCIPfreeBufferArray(scip, &vars);

   consdata->presolved = TRUE;

   return SCIP_OKAY;
}

/** analyzes conflicting assignment on given constraint, and adds conflict constraint to problem */
static
SCIP_RETCODE analyzeConflict(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< logic or constraint that detected the conflict */
   )
{
   SCIP_CONSDATA* consdata;
   int v;

   /* conflict analysis can only be applied in solving stage and if it is applicable */
   if( (SCIPgetStage(scip) != SCIP_STAGE_SOLVING && !SCIPinProbing(scip)) || !SCIPisConflictAnalysisApplicable(scip) )
      return SCIP_OKAY;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* initialize conflict analysis, and add all variables of infeasible constraint to conflict candidate queue */
   SCIP_CALL( SCIPinitConflictAnalysis(scip) );
   for( v = 0; v < consdata->nvars; ++v )
   {
      SCIP_CALL( SCIPaddConflictBinvar(scip, consdata->vars[v]) );
   }

   /* analyze the conflict */
   SCIP_CALL( SCIPanalyzeConflictCons(scip, cons, NULL) );

   return SCIP_OKAY;
}

/** disables or deletes the given constraint, depending on the current depth */
static
SCIP_RETCODE disableCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< bound disjunction constraint to be disabled */
   )
{
   assert(SCIPconsGetValidDepth(cons) <= SCIPgetDepth(scip));

   /* in case the logic or constraint is satisfied in the depth where it is also valid, we can delete it */
   if( SCIPgetDepth(scip) == SCIPconsGetValidDepth(cons) )
   {
      SCIP_CALL( SCIPdelCons(scip, cons) );
   }
   else
   {
      SCIPdebugMessage("disabling constraint cons <%s> at depth %d\n", SCIPconsGetName(cons), SCIPgetDepth(scip));
      SCIP_CALL( SCIPdisableCons(scip, cons) );
   }

   return SCIP_OKAY;
}

/** find pairs of negated variables in constraint: constraint is redundant */
/** find sets of equal variables in constraint: multiple entries of variable can be replaced by single entry */
static
SCIP_RETCODE mergeMultiples(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   unsigned char**       entries,            /**< array to store whether two positions in constraints represent the same variable */
   int*                  nentries,           /**< pointer for array size, if array will be to small it's corrected */
   SCIP_Bool*            redundant,          /**< returns whether a variable fixed to one exists in the constraint */
   int*                  nchgcoefs           /**< pointer to count number of changed/deleted coefficients */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR** vars;
   int nvars;
   SCIP_Bool* negarray;
   SCIP_VAR* var;
   int v;
   int pos;
#ifndef NDEBUG
   int nbinvars;
   int nintvars;
   int nimplvars;
#endif

   assert(scip != NULL);
   assert(cons != NULL);
   assert(eventhdlr != NULL);
   assert(*entries != NULL);
   assert(nentries != NULL);
   assert(redundant != NULL);
   assert(nchgcoefs != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   nvars = consdata->nvars;

   *redundant = FALSE;

   if( consdata->merged )
      return SCIP_OKAY;

   if( consdata->nvars <= 1 )
   {
      consdata->merged = TRUE;
      return SCIP_OKAY;
   }

   assert(consdata->vars != NULL && nvars > 0);

#ifndef NDEBUG
   nbinvars = SCIPgetNBinVars(scip);
   nintvars = SCIPgetNIntVars(scip);
   nimplvars = SCIPgetNImplVars(scip);
   assert(*nentries >= nbinvars + nintvars + nimplvars);

   /* all variables should be active or negative active variables, otherwise something went wrong with applyFixings()
    * called before mergeMultiples()
    */
   assert(consdata->presolved);
#endif

   /* allocate temporary memory */
   SCIP_CALL( SCIPallocBufferArray(scip, &negarray, nvars) );

   vars = consdata->vars;

   /* initialize entries array */
   for( v = nvars - 1; v >= 0; --v )
   {
      /* all variables should be active or negative active variables, otherwise something went wrong with applyFixings()
       * called before mergeMultiples()
       */
      assert(SCIPvarIsActive(vars[v]) ||
         (SCIPvarGetStatus(vars[v]) == SCIP_VARSTATUS_NEGATED && SCIPvarIsActive(SCIPvarGetNegationVar(vars[v]))));
      negarray[v] = SCIPvarIsNegated(vars[v]);
      var = negarray[v] ? SCIPvarGetNegationVar(vars[v]) : vars[v];
      assert(SCIPvarIsActive(var));

      pos = SCIPvarGetProbindex(var);

      /* check variable type, either pure binary or an integer/implicit integer variable with 0/1 bounds */
      assert((pos < nbinvars && SCIPvarGetType(var) == SCIP_VARTYPE_BINARY)
         || (SCIPvarIsBinary(var) &&
            ((pos >= nbinvars && pos < nbinvars + nintvars && SCIPvarGetType(var) == SCIP_VARTYPE_INTEGER) ||
               (pos >= nbinvars + nintvars && pos < nbinvars + nintvars + nimplvars &&
                  SCIPvarGetType(var) == SCIP_VARTYPE_IMPLINT))));

      /* var is not active yet */
      (*entries)[pos] = 0;
   }

   /* check all vars for multiple entries, do necessary backwards loop because deletion only affect rear items */
   for( v = nvars - 1; v >= 0; --v )
   {
      var = negarray[v] ? SCIPvarGetNegationVar(vars[v]) : vars[v];
      assert(SCIPvarIsActive(var));

      pos = SCIPvarGetProbindex(var);

      /* if var occurs first time in constraint init entries array */
      if( (*entries)[pos] == 0 )
         (*entries)[pos] = negarray[v] ? 2 : 1;
      /* if var occurs second time in constraint, first time it was not negated */
      else if( (*entries)[pos] == 1 )
      {
         if( negarray[v] )
         {
            SCIPdebugMessage("logicor constraint <%s> redundant: variable <%s> and its negation are present\n",
               SCIPconsGetName(cons), SCIPvarGetName(var));

            *redundant = TRUE;
            goto TERMINATE;
         }
         else
         {
            SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );
            ++(*nchgcoefs);
         }
      }
      /* if var occurs second time in constraint, first time it was negated */
      else
      {
         if( !negarray[v] )
         {
            SCIPdebugMessage("logicor constraint <%s> redundant: variable <%s> and its negation are present\n",
               SCIPconsGetName(cons), SCIPvarGetName(var));

            *redundant = TRUE;
            goto TERMINATE;
         }
         else
         {
            SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );
            ++(*nchgcoefs);
         }
      }
   }

 TERMINATE:
   /* free temporary memory */
   SCIPfreeBufferArray(scip, &negarray);

   consdata->merged = TRUE;

   return SCIP_OKAY;
}

/** checks constraint for violation only looking at the watched variables, applies fixings if possible */
static
SCIP_RETCODE processWatchedVars(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint to be processed */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   SCIP_Bool*            cutoff,             /**< pointer to store TRUE, if the node can be cut off */
   SCIP_Bool*            reduceddom,         /**< pointer to store TRUE, if a domain reduction was found */
   SCIP_Bool*            addcut,             /**< pointer to store whether this constraint must be added as a cut */
   SCIP_Bool*            mustcheck           /**< pointer to store whether this constraint must be checked for feasibility */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR** vars;
   SCIP_Longint nbranchings1;
   SCIP_Longint nbranchings2;
   int nvars;
   int watchedvar1;
   int watchedvar2;

   assert(cons != NULL);
   assert(SCIPconsGetHdlr(cons) != NULL);
   assert(strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) == 0);
   assert(cutoff != NULL);
   assert(reduceddom != NULL);
   assert(addcut != NULL);
   assert(mustcheck != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->watchedvar1 == -1 || consdata->watchedvar1 != consdata->watchedvar2);

   *addcut = FALSE;
   *mustcheck = FALSE;

   SCIPdebugMessage("processing watched variables of constraint <%s>\n", SCIPconsGetName(cons));

   vars = consdata->vars;
   nvars = consdata->nvars;
   assert(nvars == 0 || vars != NULL);

   /* check watched variables if they are fixed to one */
   if( consdata->watchedvar1 >= 0 && SCIPvarGetLbLocal(vars[consdata->watchedvar1]) > 0.5 )
   {
      /* the variable is fixed to one, making the constraint redundant -> disable the constraint */
      SCIPdebugMessage(" -> disabling constraint <%s> (watchedvar1 fixed to 1.0)\n", SCIPconsGetName(cons));
      SCIP_CALL( disableCons(scip, cons) );
      return SCIP_OKAY;
   }
   if( consdata->watchedvar2 >= 0 && SCIPvarGetLbLocal(vars[consdata->watchedvar2]) > 0.5 )
   {
      /* the variable is fixed to one, making the constraint redundant -> disable the constraint */
      SCIPdebugMessage(" -> disabling constraint <%s> (watchedvar2 fixed to 1.0)\n", SCIPconsGetName(cons));
      SCIP_CALL( disableCons(scip, cons) );
      return SCIP_OKAY;
   }

   /* check if watched variables are still unfixed */
   watchedvar1 = -1;
   watchedvar2 = -1;
   nbranchings1 = SCIP_LONGINT_MAX;
   nbranchings2 = SCIP_LONGINT_MAX;
   if( consdata->watchedvar1 >= 0 && SCIPvarGetUbLocal(vars[consdata->watchedvar1]) > 0.5 )
   {
      watchedvar1 = consdata->watchedvar1;
      nbranchings1 = -1; /* prefer keeping the watched variable */
   }
   if( consdata->watchedvar2 >= 0 && SCIPvarGetUbLocal(vars[consdata->watchedvar2]) > 0.5 )
   {
      if( watchedvar1 == -1 )
      {
         watchedvar1 = consdata->watchedvar2;
         nbranchings1 = -1; /* prefer keeping the watched variable */
      }
      else
      {
         watchedvar2 = consdata->watchedvar2;
         nbranchings2 = -1; /* prefer keeping the watched variable */
      }
   }
   assert(watchedvar1 >= 0 || watchedvar2 == -1);
   assert(nbranchings1 <= nbranchings2);

   /* search for new watched variables */
   if( watchedvar2 == -1 )
   {
      int v;

      for( v = 0; v < nvars; ++v )
      {
         SCIP_Longint nbranchings;

         /* don't process the watched variables again */
         if( v == consdata->watchedvar1 || v == consdata->watchedvar2 )
            continue;

         /* check, if the variable is fixed */
         if( SCIPvarGetUbLocal(vars[v]) < 0.5 )
            continue;

         /* check, if the literal is satisfied */
         if( SCIPvarGetLbLocal(vars[v]) > 0.5 )
         {
            assert(v != consdata->watchedvar1);
            assert(v != consdata->watchedvar2);

            /* the variable is fixed to one, making the constraint redundant;
             * make sure, the feasible variable is watched and disable the constraint
             */
            SCIPdebugMessage(" -> disabling constraint <%s> (variable <%s> fixed to 1.0)\n", 
               SCIPconsGetName(cons), SCIPvarGetName(vars[v]));
            if( consdata->watchedvar1 != -1 )
            {
               SCIP_CALL( switchWatchedvars(scip, cons, eventhdlr, consdata->watchedvar1, v) );
            }
            else
            {
               SCIP_CALL( switchWatchedvars(scip, cons, eventhdlr, v, consdata->watchedvar2) );
            }
            SCIP_CALL( disableCons(scip, cons) );
            return SCIP_OKAY;
         }

         /* the variable is unfixed and can be used as watched variable */
         nbranchings = SCIPvarGetNBranchingsCurrentRun(vars[v], SCIP_BRANCHDIR_DOWNWARDS);
         assert(nbranchings >= 0);
         if( nbranchings < nbranchings2 )
         {
            if( nbranchings < nbranchings1 )
            {
               watchedvar2 = watchedvar1;
               nbranchings2 = nbranchings1;
               watchedvar1 = v;
               nbranchings1 = nbranchings;
            }
            else
            {
               watchedvar2 = v;
               nbranchings2 = nbranchings;
            }
         }
      }
   }
   assert(nbranchings1 <= nbranchings2);
   assert(watchedvar1 >= 0 || watchedvar2 == -1);

   if( watchedvar1 == -1 )
   {
      /* there is no unfixed variable left -> the constraint is infeasible
       *  - a modifiable constraint must be added as a cut and further pricing must be performed in the LP solving loop
       *  - an unmodifiable constraint is infeasible and the node can be cut off
       */
      assert(watchedvar2 == -1);

      SCIPdebugMessage(" -> constraint <%s> is infeasible\n", SCIPconsGetName(cons));

      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      if( SCIPconsIsModifiable(cons) )
         *addcut = TRUE;
      else
      {
         /* use conflict analysis to get a conflict constraint out of the conflicting assignment */
         SCIP_CALL( analyzeConflict(scip, cons) );

         /* mark the node to be cut off */
         *cutoff = TRUE;
      }
   }
   else if( watchedvar2 == -1 )
   {
      /* there is only one unfixed variable:
       * - a modifiable constraint must be checked manually
       * - an unmodifiable constraint is feasible and can be disabled after the remaining variable is fixed to one
       */
      assert(0 <= watchedvar1 && watchedvar1 < nvars);
      assert(SCIPisFeasEQ(scip, SCIPvarGetLbLocal(vars[watchedvar1]), 0.0));
      assert(SCIPisFeasEQ(scip, SCIPvarGetUbLocal(vars[watchedvar1]), 1.0));
      if( SCIPconsIsModifiable(cons) )
         *mustcheck = TRUE;
      else
      {
         SCIP_Bool infbdchg;

         /* fixed remaining variable to one and disable constraint; make sure, the fixed-to-one variable is watched */
         SCIPdebugMessage(" -> single-literal constraint <%s> (fix <%s> to 1.0) at depth %d\n", 
            SCIPconsGetName(cons), SCIPvarGetName(vars[watchedvar1]), SCIPgetDepth(scip));
         SCIP_CALL( SCIPinferBinvarCons(scip, vars[watchedvar1], TRUE, cons, 0, &infbdchg, NULL) );
         assert(!infbdchg);
         SCIP_CALL( SCIPresetConsAge(scip, cons) );
         if( watchedvar1 != consdata->watchedvar1 ) /* keep one of the watched variables */
         {
            SCIP_CALL( switchWatchedvars(scip, cons, eventhdlr, watchedvar1, consdata->watchedvar1) );
         }
         SCIP_CALL( disableCons(scip, cons) );
         *reduceddom = TRUE;
      }
   }
   else
   {
      SCIPdebugMessage(" -> new watched variables <%s> and <%s> of constraint <%s> are still unfixed\n",
         SCIPvarGetName(vars[watchedvar1]), SCIPvarGetName(vars[watchedvar2]), SCIPconsGetName(cons));

      /* switch to the new watched variables */
      SCIP_CALL( switchWatchedvars(scip, cons, eventhdlr, watchedvar1, watchedvar2) );

      /* there are at least two unfixed variables -> the constraint must be checked manually */
      *mustcheck = TRUE;

      /* disable propagation of constraint until a watched variable gets fixed */
      SCIP_CALL( SCIPdisableConsPropagation(scip, cons) );

      /* increase aging counter */
      SCIP_CALL( SCIPaddConsAge(scip, cons, AGEINCREASE(consdata->nvars)) );
   }

   return SCIP_OKAY;
}

/** checks constraint for violation, returns TRUE iff constraint is feasible */
static
SCIP_RETCODE checkCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint to be checked */
   SCIP_SOL*             sol,                /**< primal CIP solution */
   SCIP_Bool*            violated            /**< pointer to store whether the given solution violates the constraint */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_VAR** vars;
   SCIP_Real solval;
   SCIP_Real sum;
   int nvars;
   int v;

   assert(violated != NULL);

   *violated = FALSE;
   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   vars = consdata->vars;
   nvars = consdata->nvars;

   /* calculate the constraint's activity */
   sum = 0.0;
   solval = 0.0;
   for( v = 0; v < nvars && sum < 1.0; ++v )
   {
      assert(SCIPvarIsBinary(vars[v]));

      solval = SCIPgetSolVal(scip, sol, vars[v]);
      assert(SCIPisFeasGE(scip, solval, 0.0) && SCIPisFeasLE(scip, solval, 1.0));

      sum += solval;
   }

   *violated = SCIPisFeasLT(scip, sum, 1.0);

   return SCIP_OKAY;
}

/** creates an LP row in a logic or constraint data object */
static
SCIP_RETCODE createRow(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< logic or constraint */
   )
{
   SCIP_CONSDATA* consdata;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->row == NULL);

   SCIP_CALL( SCIPcreateEmptyRowCons(scip, &consdata->row, SCIPconsGetHdlr(cons), SCIPconsGetName(cons), 1.0, SCIPinfinity(scip),
         SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons), SCIPconsIsRemovable(cons)) );

   SCIP_CALL( SCIPaddVarsToRowSameCoef(scip, consdata->row, consdata->nvars, consdata->vars, 1.0) );

   return SCIP_OKAY;
}

/** adds logic or constraint as cut to the LP */
static
SCIP_RETCODE addCut(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_SOL*             sol,                /**< primal CIP solution, NULL for current LP solution */
   SCIP_Bool*            cutoff              /**< whether a cutoff has been detected */
   )
{
   SCIP_CONSDATA* consdata;

   assert( cutoff != NULL );
   *cutoff = FALSE;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( consdata->row == NULL )
   {
      /* convert logic or constraint data into LP row */
      SCIP_CALL( createRow(scip, cons) );
   }
   assert(consdata->row != NULL);

   /* insert LP row as cut */
   if( !SCIProwIsInLP(consdata->row) )
   {
      SCIPdebugMessage("adding constraint <%s> as cut to the LP\n", SCIPconsGetName(cons));
      SCIP_CALL( SCIPaddCut(scip, sol, consdata->row, FALSE, cutoff) );
   }

   return SCIP_OKAY;
}

/** checks constraint for violation, and adds it as a cut if possible */
static
SCIP_RETCODE separateCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint to be separated */
   SCIP_SOL*             sol,                /**< primal CIP solution, NULL for current LP solution */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   SCIP_Bool*            cutoff,             /**< pointer to store TRUE, if the node can be cut off */
   SCIP_Bool*            separated,          /**< pointer to store TRUE, if a cut was found */
   SCIP_Bool*            reduceddom          /**< pointer to store TRUE, if a domain reduction was found */
   )
{
   SCIP_Bool addcut;
   SCIP_Bool mustcheck;

   assert(cons != NULL);
   assert(SCIPconsGetHdlr(cons) != NULL);
   assert(strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) == 0);
   assert(cutoff != NULL);
   assert(separated != NULL);
   assert(reduceddom != NULL);

   *cutoff = FALSE;
   SCIPdebugMessage("separating constraint <%s>\n", SCIPconsGetName(cons));

   /* update and check the watched variables, if they were changed since last processing */
   if( sol == NULL && SCIPconsIsPropagationEnabled(cons) )
   {
      SCIP_CALL( processWatchedVars(scip, cons, eventhdlr, cutoff, reduceddom, &addcut, &mustcheck) );
   }
   else
   {
      addcut = FALSE;
      mustcheck = TRUE;
   }

   if( mustcheck )
   {
      SCIP_CONSDATA* consdata;

      assert(!addcut);

      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);

      /* variable's fixings didn't give us any information -> we have to check the constraint */
      if( sol == NULL && consdata->row != NULL )
      {
         /* skip constraints already in the LP */
         if( SCIProwIsInLP(consdata->row) )
            return SCIP_OKAY;
         else
         {
            SCIP_Real feasibility;

            assert(!SCIProwIsInLP(consdata->row));
            feasibility = SCIPgetRowLPFeasibility(scip, consdata->row);
            addcut = SCIPisFeasNegative(scip, feasibility);
         }
      }
      else
      {
         SCIP_CALL( checkCons(scip, cons, sol, &addcut) );
      }
   }

   if( addcut )
   {
      /* insert LP row as cut */
      SCIP_CALL( addCut(scip, cons, sol, cutoff) );
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      *separated = TRUE;
   }

   return SCIP_OKAY;
}

/** enforces the pseudo solution on the given constraint */
static
SCIP_RETCODE enforcePseudo(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint to be separated */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   SCIP_Bool*            cutoff,             /**< pointer to store TRUE, if the node can be cut off */
   SCIP_Bool*            infeasible,         /**< pointer to store TRUE, if the constraint was infeasible */
   SCIP_Bool*            reduceddom,         /**< pointer to store TRUE, if a domain reduction was found */
   SCIP_Bool*            solvelp             /**< pointer to store TRUE, if the LP has to be solved */
   )
{
   SCIP_Bool addcut;
   SCIP_Bool mustcheck;

   assert(!SCIPhasCurrentNodeLP(scip));
   assert(cons != NULL);
   assert(SCIPconsGetHdlr(cons) != NULL);
   assert(strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) == 0);
   assert(cutoff != NULL);
   assert(infeasible != NULL);
   assert(reduceddom != NULL);
   assert(solvelp != NULL);

   /* update and check the watched variables, if they were changed since last processing */
   if( SCIPconsIsPropagationEnabled(cons) )
   {
      SCIP_CALL( processWatchedVars(scip, cons, eventhdlr, cutoff, reduceddom, &addcut, &mustcheck) );
   }
   else
   {
      addcut = FALSE;
      mustcheck = TRUE;
   }

   if( mustcheck )
   {
      SCIP_Bool violated;

      assert(!addcut);

      SCIP_CALL( checkCons(scip, cons, NULL, &violated) );
      if( violated )
      {
         /* constraint was infeasible -> reset age */
         SCIP_CALL( SCIPresetConsAge(scip, cons) );
         *infeasible = TRUE;
      }
   }
   else if( addcut )
   {
      /* a cut must be added to the LP -> we have to solve the LP immediately */
      SCIP_CALL( SCIPresetConsAge(scip, cons) );
      *solvelp = TRUE;
   }

   return SCIP_OKAY;
}

/** sorts logicor constraint's variables by non-decreasing variable index */
static
void consdataSort(
   SCIP_CONSDATA*        consdata            /**< linear constraint data */
   )
{
   assert(consdata != NULL);

   if( !consdata->sorted )
   {
      if( consdata->nvars <= 1 )
         consdata->sorted = TRUE;
      else
      {
         SCIP_VAR* var1 = NULL;
         SCIP_VAR* var2 = NULL;

         /* remember watch variables */
         if( consdata->watchedvar1 != -1 )
         {
            var1 = consdata->vars[consdata->watchedvar1];
            assert(var1 != NULL);
            consdata->watchedvar1 = -1;
            if( consdata->watchedvar2 != -1 )
            {
               var2 = consdata->vars[consdata->watchedvar2];
               assert(var2 != NULL);
               consdata->watchedvar2 = -1;
            }
         }
         assert(consdata->watchedvar1 == -1);
         assert(consdata->watchedvar2 == -1);
         assert(var1 != NULL || var2 == NULL);

         /* sort variables after index */
         SCIPsortPtr((void**)consdata->vars, SCIPvarComp, consdata->nvars);
         consdata->sorted = TRUE;

         /* correct watched variables */
         if( var1 != NULL )
         {
            int pos;
#ifndef NDEBUG
            SCIP_Bool found;

            found = SCIPsortedvecFindPtr((void**)consdata->vars, SCIPvarComp, (void*)var1, consdata->nvars, &pos);
            assert(found);
#else
            SCIPsortedvecFindPtr((void**)consdata->vars, SCIPvarComp, (void*)var1, consdata->nvars, &pos);
#endif
            assert(pos >= 0 && pos < consdata->nvars);
            consdata->watchedvar1 = pos;

            if( var2 != NULL )
            {
#ifndef NDEBUG
               found = SCIPsortedvecFindPtr((void**)consdata->vars, SCIPvarComp, (void*)var2, consdata->nvars, &pos);
               assert(found);
#else
               SCIPsortedvecFindPtr((void**)consdata->vars, SCIPvarComp, (void*)var2, consdata->nvars, &pos);
#endif
               assert(pos >= 0 && pos < consdata->nvars);
               consdata->watchedvar2 = pos;
            }
         }
      }
   }

#ifdef SCIP_DEBUG
   /* check sorting */
   {
      int v;

      for( v = consdata->nvars - 1; v > 0; --v )
      {
         assert(SCIPvarCompare(consdata->vars[v], consdata->vars[v - 1]) >= 0);
      }
   }
#endif
}

/** gets the key of the given element */
static
SCIP_DECL_HASHGETKEY(hashGetKeyLogicorcons)
{  /*lint --e{715}*/
   /* the key is the element itself */
   return elem;
}

/** returns TRUE iff both keys are equal; two constraints are equal if they have the same variables */
static
SCIP_DECL_HASHKEYEQ(hashKeyEqLogicorcons)
{
   SCIP_CONSDATA* consdata1;
   SCIP_CONSDATA* consdata2;
   SCIP_Bool coefsequal;
   int i;
#ifndef NDEBUG
   SCIP* scip;

   scip = (SCIP*)userptr;
   assert(scip != NULL);
#endif

   consdata1 = SCIPconsGetData((SCIP_CONS*)key1);
   consdata2 = SCIPconsGetData((SCIP_CONS*)key2);

   /* checks trivial case */
   if( consdata1->nvars != consdata2->nvars )
      return FALSE;

   /* sorts the constraints */
   consdataSort(consdata1);
   consdataSort(consdata2);
   assert(consdata1->sorted);
   assert(consdata2->sorted);

   coefsequal = TRUE;

   for( i = 0; i < consdata1->nvars ; ++i )
   {
      /* tests if variables are equal */
      if( consdata1->vars[i] != consdata2->vars[i] )
      {
         assert(SCIPvarCompare(consdata1->vars[i], consdata2->vars[i]) == 1 ||
            SCIPvarCompare(consdata1->vars[i], consdata2->vars[i]) == -1);
         coefsequal = FALSE;
         break;
      }
      assert(SCIPvarCompare(consdata1->vars[i], consdata2->vars[i]) == 0);
   }

   return coefsequal;
}

/** returns the hash value of the key */
static
SCIP_DECL_HASHKEYVAL(hashKeyValLogicorcons)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;
   unsigned int hashval;
   int minidx;
   int mididx;
   int maxidx;

   consdata = SCIPconsGetData((SCIP_CONS*)key);
   assert(consdata != NULL);
   assert(consdata->sorted);
   assert(consdata->nvars > 0);

   minidx = SCIPvarGetIndex(consdata->vars[0]);
   mididx = SCIPvarGetIndex(consdata->vars[consdata->nvars / 2]);
   maxidx = SCIPvarGetIndex(consdata->vars[consdata->nvars - 1]);
   assert(minidx >= 0 && minidx <= maxidx);

   hashval = (consdata->nvars << 29) + (minidx << 22) + (mididx << 11) + maxidx; /*lint !e701*/

   return hashval;
}

/** compares each constraint with all other constraints for a possible duplication and removes duplicates using a hash
 *  table; also @see removeRedundantConssAndNonzeros()
 */
static
SCIP_RETCODE detectRedundantConstraints(
   SCIP*                 scip,               /**< SCIP data structure */
   BMS_BLKMEM*           blkmem,             /**< block memory */
   SCIP_CONS**           conss,              /**< constraint set */
   int                   nconss,             /**< number of constraints in constraint set */
   int*                  firstchange,        /**< pointer to store first changed constraint */
   int*                  ndelconss           /**< pointer to count number of deleted constraints */
)
{
   SCIP_HASHTABLE* hashtable;
   int hashtablesize;
   int c;

   assert(conss != NULL);
   assert(ndelconss != NULL);

   /* create a hash table for the constraint set */
   hashtablesize = SCIPcalcHashtableSize(10*nconss);
   hashtablesize = MAX(hashtablesize, HASHSIZE_LOGICORCONS);
   SCIP_CALL( SCIPhashtableCreate(&hashtable, blkmem, hashtablesize,
         hashGetKeyLogicorcons, hashKeyEqLogicorcons, hashKeyValLogicorcons, (void*) scip) );

   /* check all constraints in the given set for redundancy */
   for( c = 0; c < nconss; ++c )
   {
      SCIP_CONS* cons0;
      SCIP_CONS* cons1;
      SCIP_CONSDATA* consdata0;

      cons0 = conss[c];

      if( !SCIPconsIsActive(cons0) || SCIPconsIsModifiable(cons0) )
         continue;

      consdata0 = SCIPconsGetData(cons0);
      /* sort the constraint */
      consdataSort(consdata0);
      assert(consdata0->sorted);

      /* get constraint from current hash table with same variables as cons0 */
      cons1 = (SCIP_CONS*)(SCIPhashtableRetrieve(hashtable, (void*)cons0));

      if( cons1 != NULL )
      {
#ifndef NDEBUG
         SCIP_CONSDATA* consdata1;
#endif

         assert(SCIPconsIsActive(cons1));
         assert(!SCIPconsIsModifiable(cons1));

#ifndef NDEBUG
         consdata1 = SCIPconsGetData(cons1);
#endif
         assert(consdata0 != NULL && consdata1 != NULL);
         assert(consdata0->nvars >= 1 && consdata0->nvars == consdata1->nvars);

         assert(consdata0->sorted && consdata1->sorted);
         assert(consdata0->vars[0] == consdata1->vars[0]);

         /* update flags of constraint which caused the redundancy s.t. nonredundant information doesn't get lost */
         SCIP_CALL( SCIPupdateConsFlags(scip, cons1, cons0) );

         /* delete consdel */
         SCIP_CALL( SCIPdelCons(scip, cons0) );
         (*ndelconss)++;

         /* update the first changed constraint to begin the next aggregation round with */
         if( consdata0->changed && SCIPconsGetPos(cons1) < *firstchange )
            *firstchange = SCIPconsGetPos(cons1);

         assert(SCIPconsIsActive(cons1));
      }
      else
      {
         /* no such constraint in current hash table: insert cons0 into hash table */  
         SCIP_CALL( SCIPhashtableInsert(hashtable, (void*) cons0) );
      }
   }

   /* free hash table */
   SCIPhashtableFree(&hashtable);

   return SCIP_OKAY;
}

/** removes the redundant second constraint and updates the flags of the first one */
static
SCIP_RETCODE removeRedundantCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons0,              /**< constraint that should stay */
   SCIP_CONS*            cons1,              /**< constraint that should be deleted */
   int*                  ndelconss           /**< pointer to count number of deleted constraints */
   )
{
   assert(ndelconss != NULL);

   SCIPdebugMessage(" -> removing logicor constraint <%s> which is redundant to <%s>\n",
      SCIPconsGetName(cons1), SCIPconsGetName(cons0));
   SCIPdebugPrintCons(scip, cons0, NULL);
   SCIPdebugPrintCons(scip, cons1, NULL);

   /* update flags of cons0 */
   SCIP_CALL( SCIPupdateConsFlags(scip, cons0, cons1) );

   /* delete cons1 */
   SCIP_CALL( SCIPdelCons(scip, cons1) );
   (*ndelconss)++;

   return SCIP_OKAY;
}


/** compute and return a signature for given variables */
static
unsigned int calcSignature(
   SCIP_VAR**            vars,               /**< variables to calculate the signature for */
   int                   nvars               /**< number of variables to calculate the signature for */
   )
{
   unsigned int signature = 0;
   int v;

   assert(vars != NULL);
   assert(nvars >= 1);

   for( v = nvars - 1; v >= 0; --v )
   {
      signature |= ((unsigned int)1 << ((unsigned int)SCIPvarGetIndex(vars[v]) % (sizeof(unsigned int) * 8)));
   }

   return signature;
}

/** compute the constraint signature which is used to detect constraints, that contain potentially the same set of
 *  variables
 */
static
void consdataCalcSignature(
   SCIP_CONSDATA*        consdata            /**< logicor constraint data */
   )
{
   if( consdata->validsignature )
      return;

   consdata->signature = calcSignature(consdata->vars, consdata->nvars);
   consdata->validsignature = TRUE;
}

/** remove a constraint from the column representation */
static
void removeConsFromOccurList(
   SCIP_CONS*            cons,               /**< logicor constraint */
   SCIP_HASHMAP*         varstopos,          /**< map for mapping variables to positions in the occurlist */
   SCIP_CONS***          occurlist,          /**< column representation of logicor constraints */
   int*                  noccurlistentries,  /**< arrray with number of constraints for each variable in the occurlist */
   int                   occurlistlength     /**< number of columns in the occurlist */
   )
{
   SCIP_VAR** vars;
   SCIP_VAR* var;
   SCIP_CONSDATA* consdata;
   int nvars;
   int pos;
   int v;
   int l;

   assert(cons != NULL);
   assert(SCIPconsIsActive(cons));
   assert(varstopos != NULL);
   assert(occurlist != NULL);
   assert(noccurlistentries != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   nvars = consdata->nvars;
   assert(nvars >= 1);
   vars = consdata->vars;
   assert(vars != NULL);

   /* remove constraint from list */
   for( v = nvars - 1; v >= 0; --v )
   {
      var = vars[v];

      assert(SCIPhashmapExists(varstopos, (void*) var));

      pos = (int) (size_t) SCIPhashmapGetImage(varstopos, (void*)var);
      assert(0 < pos && pos <= occurlistlength);

      --pos;

      /* remove for each variable one corresponding entry */
      for( l = noccurlistentries[pos] - 1; l >= 0; --l )
      {
         if( occurlist[pos][l] == cons )
         {
            --noccurlistentries[pos];
            assert(noccurlistentries[pos] >= 0);

            occurlist[pos][l] = occurlist[pos][noccurlistentries[pos]];
            break;
         }
      }
      assert(l >= 0);
   }
}

/** determine shortest constraint list in column representation */
static
void findShortestOccurlist(
   SCIP_VAR**            vars,               /**< variables to find the shortestlist for */
   int                   nvars,              /**< number of variables */
   SCIP_HASHMAP*         varstopos,          /**< map for mapping variables to positions in the occurlist */
   SCIP_CONS***          occurlist,          /**< column representation of logicor constraints */
   int*                  noccurlistentries,  /**< arrray with number of constraints for each variable in the occurlist */
   int                   occurlistlength,    /**< number of columns in the occurlist */
   int*                  nentries,           /**< pointer to store the number of entries in the shortest list */
   SCIP_CONS***          shortestlist        /**< pointer to store smallest array with constraints */
   )
{
   SCIP_VAR* var;
   int pos;
   int v;

   assert(vars != 0);
   assert(nvars >= 1);
   assert(varstopos != NULL);
   assert(occurlist != NULL);
   assert(noccurlistentries != NULL);
   assert(nentries != NULL);
   assert(shortestlist != NULL);

   *nentries = INT_MAX;
   *shortestlist = NULL;

   /* find the shortest list */
   for( v = nvars - 1; v >= 0; --v )
   {
      var = vars[v];
      assert(var != NULL);

      /* it might be that a variable is not yet put into the occurlist, then this constraint cannot cover another */
      if( !SCIPhashmapExists(varstopos, (void*) var) )
      {
         *nentries = 0;
         return;
      }

      pos = (int) (size_t) SCIPhashmapGetImage(varstopos, (void*)var);
      assert(0 < pos && pos <= occurlistlength);

      --pos;

      /* remember the shortest list */
      if( noccurlistentries[pos] < *nentries )
      {
         *nentries = noccurlistentries[pos];
         *shortestlist = occurlist[pos];
      }
   }
}

/** run a pairwise comparison for detecting subset-constraints of other constraint while using a signature */
static
SCIP_RETCODE removeRedundantConss(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logicor constraint to check if it covers another */
   SCIP_HASHMAP*         varstopos,          /**< map for mapping variables to positions in the occurlist */
   SCIP_CONS***          occurlist,          /**< column representation of logicor constraints */
   int*                  noccurlistentries,  /**< arrray with number of constraints for each variable in the occurlist */
   int                   occurlistlength,    /**< number of columns in the occurlist */
   int*                  ndelconss           /**< pointer to store the number of deleted constraints */
   )
{
   SCIP_CONS** shortestlist;
   SCIP_VAR** vars;
   SCIP_CONS* cons1;
   SCIP_VAR* var;
   SCIP_CONSDATA* consdata;
   int nentries;
   int c;
   int v;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(SCIPconsIsActive(cons));
   assert(!SCIPconsIsModifiable(cons));
   assert(varstopos != NULL);
   assert(occurlist != NULL);
   assert(noccurlistentries != NULL);
   assert(ndelconss != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->nvars > 1);
   assert(consdata->validsignature);
   assert(consdata->sorted);

   vars = consdata->vars;
   assert(vars != NULL);

   /* determine shortest column */
   findShortestOccurlist(vars, consdata->nvars, varstopos, occurlist, noccurlistentries, occurlistlength, &nentries, &shortestlist);

   /* one variable which does not appear in the column representation anymore */
   if( nentries == 0 )
      return SCIP_OKAY;

   assert(shortestlist != NULL);
   assert(0 < nentries);

   /* check all constraints in the shortest list for coverage */
   for( c = nentries - 1; c >= 0; --c )
   {
      cons1 = shortestlist[c];
      assert(cons1 != NULL);
      assert(!SCIPconsIsModifiable(cons1));
      assert(SCIPconsIsActive(cons1));

      if( cons != cons1 )
      {
         SCIP_CONSDATA* consdata1 = SCIPconsGetData(cons1);
         assert(consdata1 != NULL);
         assert(consdata1->nvars >= consdata->nvars);

         /* constraints with the same length cannot be covered and same constraints are removed in
          * detectRedundantConstraints()
          */
         if( consdata1->nvars == consdata->nvars )
            continue;

         assert(consdata->validsignature);
         assert(consdata->sorted);
         assert(consdata1->validsignature);
         assert(consdata1->sorted);

         if( (consdata->signature & (~consdata1->signature)) == 0 )
         {
            SCIP_VAR* var1;
            int v1;

            v = 0;
            v1 = 0;

            while( v < consdata->nvars && v1 < consdata1->nvars )
            {
               int comp;

               var = vars[v];
               var1 = consdata1->vars[v1];

               comp = SCIPvarCompare(var, var1);

               if( comp == 0 )
               {
                  ++v;
                  ++v1;
               }
               else if( comp > 0 )
                  ++v1;
               else
                  break;
            }

            /* cons1 is covered by cons */
            if( v == consdata->nvars )
            {
               /* remove cons1 from columns representation */
               removeConsFromOccurList(cons1, varstopos, occurlist, noccurlistentries, occurlistlength);

               /* delete redundant constraint and update constraint flags if necessary */
               SCIP_CALL( removeRedundantCons(scip, cons, cons1, ndelconss) );
            }
         }
      }
   }

   return SCIP_OKAY;
}

/** compararer for sorting constraints after their number of variables */
static
SCIP_DECL_SORTPTRCOMP(conssLogicorComp)
{
   SCIP_CONSDATA* consdata1;
   SCIP_CONSDATA* consdata2;

   assert(elem1 != NULL);
   assert(elem2 != NULL);

   consdata1 = SCIPconsGetData((SCIP_CONS*) elem1);
   consdata2 = SCIPconsGetData((SCIP_CONS*) elem2);

   assert(consdata1 != NULL);
   assert(consdata2 != NULL);

   return consdata1->nvars - consdata2->nvars;
}

/** add a constraint to the column representation */
static
SCIP_RETCODE addConsToOccurList(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logicor constraint */
   SCIP_HASHMAP*         varstopos,          /**< map for mapping variables to positions in the occurlist */
   SCIP_CONS***          occurlist,          /**< column representation of logicor constraints */
   int*                  noccurlistentries,  /**< arrray with number of constraints for each variable in the occurlist */
   int*                  occurlistsizes,     /**< array of sizes for each variable in the occurlist */
   int*                  occurlistlength,    /**< number of columns in the occurlist */
   int                   occurlistsize       /**< size of occurlist */
   )
{
   SCIP_VAR** vars;
   SCIP_VAR* var;
   SCIP_CONSDATA* consdata;
   int pos;
   int v;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(SCIPconsIsActive(cons));
   assert(varstopos != NULL);
   assert(occurlist != NULL);
   assert(noccurlistentries != NULL);
   assert(occurlistsizes != NULL);
   assert(occurlistlength != NULL);
   assert(*occurlistlength <= occurlistsize);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->nvars > 1);

   vars = consdata->vars;
   assert(vars != NULL);

   for( v = consdata->nvars - 1; v >= 0; --v )
   {
      var = vars[v];
      assert(var != NULL);
      assert(SCIPvarIsActive(var) || (SCIPvarGetNegatedVar(var) != NULL && SCIPvarIsActive(SCIPvarGetNegatedVar(var))));

      /* check if the variable is not yet put into the occurlist */
      if( !SCIPhashmapExists(varstopos, (void*) var) )
      {
         pos = *occurlistlength;
         assert(pos <= occurlistsize);

         /* occurlist values need to be clear */
         assert(occurlist[pos] == NULL);
         assert(noccurlistentries[pos] == 0);
         assert(occurlistsizes[pos] == 0);

         /* allocate memory */
         assert(SCIPvarGetNLocksDown(var) > 0 || !SCIPconsIsChecked(cons));
         occurlistsizes[pos] = SCIPvarGetNLocksDown(var) + 1;
         SCIP_CALL( SCIPallocBufferArray(scip, &(occurlist[pos]), occurlistsizes[pos]) ); /*lint !e866*/

         /* put constraint in list of current variable */
         occurlist[pos][noccurlistentries[pos]] = cons;
         ++(noccurlistentries[pos]);

         /* add new variable to map */
         SCIP_CALL( SCIPhashmapInsert(varstopos, var, (void*) (size_t) (pos + 1)) );

         ++(*occurlistlength);
      }
      else
      {
         pos = (int) (size_t) SCIPhashmapGetImage(varstopos, (void*)var);
         assert(0 < pos && pos <= *occurlistlength);

         --pos;

         assert(occurlist[pos] != NULL);
         assert(occurlistsizes[pos] > 0);

         /* do we need to resize the array */
         if( noccurlistentries[pos] == occurlistsizes[pos] )
         {
            occurlistsizes[pos] = SCIPcalcMemGrowSize(scip, occurlistsizes[pos] + 1);
            assert(occurlistsizes[pos] > noccurlistentries[pos] && occurlistsizes[pos] < INT_MAX);

            /* resize occurlist for current variable */
            SCIP_CALL( SCIPreallocBufferArray(scip, &(occurlist[pos]), occurlistsizes[pos]) ); /*lint !e866*/
         }
         assert(noccurlistentries[pos] < occurlistsizes[pos]);

         /* put constraint in list of current variable */
         occurlist[pos][noccurlistentries[pos]] = cons;
         ++(noccurlistentries[pos]);
      }
   }

   return SCIP_OKAY;
}

/** run a pairwise comparison for the given variables against all constraits to detect redundant non-zeros in these
 *  constraints
 */
static
SCIP_RETCODE removeRedundantNonZeros(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logicor constraint to check if it covers another */
   SCIP_VAR*             artvar,             /**< artificial negated variable of constraint */
   int                   artpos,             /**< position to replace constraint variable with artvar */
   SCIP_HASHMAP*         varstopos,          /**< map for mapping variables to positions in the occurlist */
   SCIP_CONS***          occurlist,          /**< column representation of logicor constraints */
   int*                  noccurlistentries,  /**< number of constraints for each variable in the occurlist */
   int                   occurlistlength,    /**< number of columns in the occurlist */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler */
   int*                  nchgcoefs,          /**< pointer to store the number of deleted non-zeros */
   SCIP_Bool*            deleted             /**< pointer to store if cons will be deleted */
   )
{
   SCIP_CONS** shortestlist;
   SCIP_VAR** vars;
   SCIP_CONS* cons1;
   SCIP_VAR* oldvar;
   SCIP_VAR* var;
   SCIP_CONSDATA* consdata;
   unsigned int signature;
   int nentries;
   int nvars;
   int c;
   int v;
   int pos;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(artvar != NULL);
   assert(SCIPconsIsActive(cons));
   assert(!SCIPconsIsModifiable(cons));
   assert(varstopos != NULL);
   assert(SCIPhashmapExists(varstopos, (void*) artvar));
   assert(occurlist != NULL);
   assert(noccurlistentries != NULL);
   assert(nchgcoefs != NULL);
   assert(deleted != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->sorted);

   nvars = consdata->nvars;
   assert(nvars > 1);
   assert(0 <= artpos && artpos < nvars);

   vars = consdata->vars;
   assert(vars != NULL);

   *deleted = FALSE;

   /* temporary exchange the variable for finding the shortest list */
   oldvar = vars[artpos];
   assert(oldvar == SCIPvarGetNegatedVar(artvar));
   vars[artpos] = artvar;

   /* determine shortest column */
   findShortestOccurlist(vars, nvars, varstopos, occurlist, noccurlistentries, occurlistlength, &nentries, &shortestlist);

   /* correct exchanged variable with constraint variables */
   vars[artpos] = oldvar;

   /* one variable which does not appear in the column representation anymore */
   if( nentries == 0 )
      return SCIP_OKAY;

   assert(shortestlist != NULL);
   assert(0 < nentries);

   /* temporary exchange the variable for calculating a valid signature */
   oldvar = vars[artpos];
   vars[artpos] = artvar;
   signature = calcSignature(vars, nvars);

   /* correct exchanged variable with constraint variables */
   vars[artpos] = oldvar;

   /* check all constraints in the shortest list for coverage */
   for( c = nentries - 1; c >= 0; --c )
   {
      cons1 = shortestlist[c];
      assert(cons1 != NULL);
      assert(!SCIPconsIsModifiable(cons1));

      if( !SCIPconsIsActive(cons1) )
         continue;

      if( cons != cons1 )
      {
         SCIP_CONSDATA* consdata1 = SCIPconsGetData(cons1);
         assert(consdata1 != NULL);

         /* constraints with the less variables cannot be covered */
         if( consdata1->nvars < nvars )
            continue;

         pos = -1;

         assert(consdata->sorted);
         assert(consdata->merged);
         assert(consdata1->validsignature);
         assert(consdata1->sorted);
         assert(consdata1->merged);

         if( (signature & (~consdata1->signature)) == 0 )
         {
            SCIP_VAR* var1;
            int v1;

            v = 0;
            v1 = 0;

            while( v < nvars && v1 < consdata1->nvars )
            {
               int comp;

               /* skip position of artificial variable */
               if( artpos == v )
               {
                  ++v;
                  continue;
               }

               var1 = consdata1->vars[v1];

               /* did we find the artificial variable in cons1 */
               if( artvar == var1 )
               {
                  /* remember of possible redundant variable */
                  assert(pos == -1);
                  pos = v1;

                  ++v1;
                  continue;
               }

               var = vars[v];
               comp = SCIPvarCompare(var, var1);

               /* check if the cons1 can still be covered */
               if( comp == 0 )
               {
                  ++v;
                  ++v1;
               }
               else if( comp > 0 )
                  ++v1;
               else
                  break;
            }

            /* cons1 is might be covered by the changed constraints cons, meaning that we might remove the artvar from
             * cons1
             */
            if( v == nvars )
            {
               int l;

               /* if the artificial variable was not yet found, search over the rear variables in constraint cons1 */
               if( pos == -1 )
               {
                  while( v1 < consdata1->nvars )
                  {
                     if( artvar == consdata1->vars[v1] )
                     {
                        /* remember of possible redundant variable */
                        pos = v1;
                        break;
                     }
                     ++v1;
                  }
               }

               if( pos >= 0 )
               {
                  int conspos;

                  assert(pos < consdata1->nvars);
                  assert(artvar == consdata1->vars[pos]);

                  /* remove redudant entry in cons1 */
                  SCIPdebugMessage("variable %s in logicor constraint <%s> is redundant and will be removed (used constraint %s)\n", SCIPvarGetName(artvar), SCIPconsGetName(cons1), SCIPconsGetName(cons));
                  SCIPdebugPrintCons(scip, cons1, NULL);
                  conspos = pos;

                  if( consdata1->nvars > nvars )
                  {
                     pos = (int) (size_t) SCIPhashmapGetImage(varstopos, (void*)artvar);
                     assert(0 < pos && pos <= occurlistlength);

                     --pos;

                     /* remove corresponding entry in column representation */
                     for( l = noccurlistentries[pos] - 1; l >= 0; --l )
                     {
                        if( occurlist[pos][l] == cons1 )
                        {
                           --noccurlistentries[pos];
                           assert(noccurlistentries[pos] >= 0);

                           occurlist[pos][l] = occurlist[pos][noccurlistentries[pos]];
                           break;
                        }
                     }
                     assert(l >= 0);
                  }
                  else
                  {
                     assert(consdata1->nvars == nvars);

                     /* delete cons */
                     SCIPdebugMessage("logicor constraint <%s> is redundant due to constraint <%s> after removing variable <%s>\n", SCIPconsGetName(cons), SCIPconsGetName(cons1), SCIPvarGetName(artvar));

                     /* remove cons from columns representation */
                     removeConsFromOccurList(cons, varstopos, occurlist, noccurlistentries, occurlistlength);

                     /* update flags of cons1 */
                     SCIP_CALL( SCIPupdateConsFlags(scip, cons1, cons) );

                     SCIP_CALL( SCIPdelCons(scip, cons) );
                     *deleted = TRUE;
                  }

                  /* remove variable */
                  SCIP_CALL( delCoefPos(scip, cons1, eventhdlr, conspos) );
                  ++(*nchgcoefs);
                  consdataSort(consdata1);
                  consdataCalcSignature(consdata1);

                  if( *deleted )
                     return SCIP_OKAY;
               }
            }
         }
      }
   }

   return SCIP_OKAY;
}

/** find and remove redundant non-zero entries */
static
SCIP_RETCODE strengthenConss(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           conss,              /**< sorted array of logicor constraint */
   int                   nconss,             /**< number of sorted constraints */
   SCIP_HASHMAP*         varstopos,          /**< map for mapping variables to positions in the occurlist */
   SCIP_CONS***          occurlist,          /**< column representation of logicor constraints */
   int*                  noccurlistentries,  /**< number of constraints for each variable in the occurlist */
   int                   occurlistlength,    /**< number of columns in the occurlist */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   int*                  ndelconss,          /**< pointer to store the number of deleted constraints */
   int*                  nchgcoefs           /**< pointer to store the number of remove coefficients */
   )
{
   SCIP_VAR** vars;
   SCIP_CONSDATA* consdata;
   SCIP_CONS* cons;
   SCIP_VAR* artvar;
   int nvars;
   int c;
   int v;

   assert(scip != NULL);
   assert(conss != NULL || nconss == 0);
   assert(varstopos != NULL);
   assert(occurlist != NULL);
   assert(noccurlistentries != NULL);
   assert(eventhdlr != NULL);
   assert(ndelconss != NULL);
   assert(nchgcoefs != NULL);

   if( nconss == 0 )
      return SCIP_OKAY;

   assert(conss != NULL);

   for( c = 0; c < nconss; ++c )
   {
      cons = conss[c];
      assert(cons != NULL);
      assert(!SCIPconsIsModifiable(cons));

      if( !SCIPconsIsActive(cons) )
         continue;

      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);

      nvars = consdata->nvars;
      assert(nvars >= 1);

      if( nvars == 1 )
         continue;

      vars = consdata->vars;
      assert(vars != NULL);

      for( v = nvars - 1; v >= 0; --v )
      {
         artvar = SCIPvarGetNegatedVar(vars[v]);

         if( artvar != NULL && SCIPhashmapExists(varstopos, (void*) artvar) )
         {
            SCIP_Bool deleted;

            /* detect and remove redundant non-zero entries */
            /* @todo: improve this algorithm by using the information that a constraint variables does not appaer in any
             *        other constraint, which means that only this variable needs to be negated to check for redundant
             *        non-zeros, therefor change also findShortestOccurlist() to return the corresponding
             *        variable/position
             */
            SCIP_CALL( removeRedundantNonZeros(scip, cons, artvar, v, varstopos, occurlist, noccurlistentries,
            occurlistlength, eventhdlr, nchgcoefs, &deleted) );

            if( deleted )
            {
               assert(SCIPconsIsDeleted(cons));
               ++(*ndelconss);
               break;
            }
            else
               assert(SCIPconsIsActive(cons));
         }
      }
   }

   return SCIP_OKAY;
}


/** prepares a constraint by removing fixings and merge it */
static
SCIP_RETCODE prepareCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   unsigned char**       entries,            /**< array to store whether two positions in constraints represent the same variable */
   int*                  nentries,           /**< pointer for array size, if array will be to small it's corrected */
   SCIP_Bool*            redundant,          /**< returns whether a variable fixed to one exists in the constraint */
   int*                  nfixedvars,         /**< pointer to count number of fixings */
   int*                  nchgcoefs,          /**< pointer to count number of changed/deleted coefficients */
   int*                  ndelconss,          /**< pointer to count number of deleted constraints */
   SCIP_Bool*            cutoff              /**< pointer to store, if cut off appeared */
   )
{
   SCIP_CONSDATA* consdata;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(!SCIPconsIsDeleted(cons));
   assert(eventhdlr != NULL);
   assert(*entries != NULL);
   assert(nentries != NULL);
   assert(redundant != NULL);
   assert(nfixedvars != NULL);
   assert(nchgcoefs != NULL);
   assert(ndelconss != NULL);
   assert(redundant != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->nvars > 0);

   *redundant = FALSE;

   /* remove old fixings */
   if( !consdata->presolved )
   {
      /* remove all variables that are fixed to zero, check redundancy due to fixed-to-one variable */
      SCIP_CALL( applyFixings(scip, cons, eventhdlr, redundant, nchgcoefs, NULL, NULL) );
   }

   if( !*redundant )
   {
      /* merge constraint */
      SCIP_CALL( mergeMultiples(scip, cons, eventhdlr, entries, nentries, redundant, nchgcoefs) );
   }

   if( *redundant )
   {
      SCIP_CALL( SCIPdelCons(scip, cons) );
      ++(*ndelconss);

      return SCIP_OKAY;
   }

   if( consdata->nvars == 0 )
   {
      *cutoff = TRUE;
   }
   else if( consdata->nvars == 1 )
   {
      SCIP_Bool infeasible;
      SCIP_Bool fixed;

      SCIPdebugMessage(" -> fix last remaining variable and delete constraint\n");

      SCIP_CALL( SCIPfixVar(scip, consdata->vars[0], 1.0, &infeasible, &fixed) );
      assert(!infeasible);
      assert(fixed);
      ++(*nfixedvars);

      SCIP_CALL( SCIPdelCons(scip, cons) );
      ++(*ndelconss);

      *redundant = TRUE;
   }
   consdata->presolved = TRUE;

   return SCIP_OKAY;
}

#define HASHTABLESIZE_FACTOR 5

/** find covered/subsumed constraints and redundant non-zero entries
 *
 *  covered:
 *  e.g.: c1: x1 + x2 + x3 >= 1
 *        c2: x1 + x2 + x3 + x4 >= 1
 *
 *  strengthen:
 *  e.g.: c1: x1 + x2 + x3 >= 1
 *        c2: x1 + x2 + ~x3 + x4 >= 1
 *
 *     => c2: x1 + x2 + x4 >= 1
 *
 *  @see "Effective Preprocessing in SAT through Variable and Clause Elimination" by Niklas En and Armin Biere
 */
static
SCIP_RETCODE removeRedundantConssAndNonzeros(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           conss,              /**< array of logicor constraints */
   int                   nconss,             /**< number of logicor constraints */
   unsigned char**       entries,            /**< array to store whether two positions in constraints represent the same
                                              *   variable */
   int*                  nentries,           /**< pointer for array size, if array will be to small it's corrected */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   SCIP_Bool             usestrengthening,   /**< should we try to strengthen constraints by removing superflous
                                              *   non-zeros? */
   int*                  firstchange,        /**< pointer to store first changed constraint */
   int*                  nfixedvars,         /**< pointer to count number of fixings */
   int*                  ndelconss,          /**< pointer to store the number of deleted constraints */
   int*                  nchgcoefs,          /**< pointer to store the number of deleted coefficients */
   SCIP_Bool*            cutoff              /**< pointer to store, if cut off appeared */
   )
{
   SCIP_CONS*** occurlist;
   SCIP_CONS** myconss;
   SCIP_HASHMAP* varstopos;
   SCIP_CONS* cons;
   SCIP_CONSDATA* consdata;
   int* noccurlistentries;
   int* occurlistsizes;
   SCIP_Bool redundant;
   SCIP_Bool conschanged;
   int nbinvars;
   int occurlistlength;
   int occurlistsize;
   int nmyconss;
   int nmaxvars;
   int c;

   assert(scip != NULL);
   assert(conss != NULL || nconss == 0);
   assert(entries != NULL);
   assert(*entries != NULL);
   assert(nentries != NULL);
   assert(eventhdlr != NULL);
   assert(firstchange != NULL);
   assert(0 <= *firstchange);
   assert(nfixedvars != NULL);
   assert(ndelconss != NULL);
   assert(nchgcoefs != NULL);

   if( *firstchange > nconss || nconss < 2 )
      return SCIP_OKAY;

   SCIPdebugMessage("starting removeRedundantConssAndNonzeros(), pairwise comparison to detect covered logicor constraints\n");

   /* copy constraints to re-order them */
   SCIP_CALL( SCIPduplicateBufferArray(scip, &myconss, conss, nconss) );

   nmyconss = nconss;
   for( c = nconss - 1; c >= 0; --c )
   {
      cons = myconss[c];
      assert(cons != NULL);

      if( SCIPconsIsDeleted(cons) || SCIPconsIsModifiable(cons) )
      {
         myconss[c] = myconss[nmyconss - 1];
         --nmyconss;

         continue;
      }

      /* prepare constraint by removing fixings and merge it */
      SCIP_CALL( prepareCons(scip, cons, eventhdlr, entries, nentries, &redundant, nfixedvars, nchgcoefs, ndelconss, cutoff) );

      if( redundant )
      {
         assert(SCIPconsIsDeleted(cons));

         myconss[c] = myconss[nmyconss - 1];
         --nmyconss;
      }

      if( *cutoff )
      {
         SCIPfreeBufferArray(scip, &myconss);

         return SCIP_OKAY;
      }

      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);
      assert(consdata->nvars >= 2);

      /* sort the constraint */
      consdataSort(consdata);
   }

   SCIPsortPtr((void**)myconss, conssLogicorComp, nmyconss);
   assert(myconss[0] != NULL && myconss[nmyconss - 1] != NULL);
   assert(SCIPconsGetData(myconss[0]) != NULL && SCIPconsGetData(myconss[nmyconss - 1]) != NULL);
   assert(SCIPconsGetData(myconss[0])->nvars <= SCIPconsGetData(myconss[nmyconss - 1])->nvars);

   /* we can stop if strengthening is disabled and all constraints have the same amount of variables */
   if( !usestrengthening && SCIPconsGetData(myconss[0])->nvars == SCIPconsGetData(myconss[nmyconss - 1])->nvars )
   {
      SCIPfreeBufferArray(scip, &myconss);

      return SCIP_OKAY;
   }

   /* @note: in the following we have at least number of nonzeros in logicor constraints + three times two the number of
    *        binary variables memory consumption + a map for variables to positions, we need this to get a column base
    *        representation
    */

   /* get number of all possible(incl. implcit) binary variables and their negation */
   nbinvars = SCIPgetNVars(scip) - SCIPgetNContVars(scip);
   occurlistsize = 2 * nbinvars;

   /* allocate memory for the column representation for each variable */
   SCIP_CALL( SCIPallocBufferArray(scip, &occurlist, occurlistsize) );
   BMSclearMemoryArray(occurlist, occurlistsize);
   SCIP_CALL( SCIPallocBufferArray(scip, &noccurlistentries, occurlistsize) );
   BMSclearMemoryArray(noccurlistentries, occurlistsize);
   SCIP_CALL( SCIPallocBufferArray(scip, &occurlistsizes, occurlistsize) );
   BMSclearMemoryArray(occurlistsizes, occurlistsize);

   /* create hashmap to map all occuring variables to a position in the list */
   SCIP_CALL( SCIPhashmapCreate(&varstopos, SCIPblkmem(scip), SCIPcalcHashtableSize(HASHTABLESIZE_FACTOR * nmyconss)) );

   /* get maximal number of variables over all logicor constraints */
   c = nmyconss - 1;
   cons = myconss[c];
   assert(cons != NULL);
   assert(SCIPconsIsActive(cons));
   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   nmaxvars = consdata->nvars;

   occurlistlength = 0;
   conschanged = FALSE;

   /* determine all constraints with the maximal number of variables and add them to the column representation */
   do
   {
      /* calculate hash-signature */
      consdataCalcSignature(consdata);
      assert(consdata->validsignature);
      conschanged = conschanged || consdata->changed;
      consdata->changed = FALSE;

      /* add constraint to column data structure */
      SCIP_CALL( addConsToOccurList(scip, cons, varstopos, occurlist, noccurlistentries, occurlistsizes, &occurlistlength, occurlistsize) );

      --c;
      if( c < 0 )
         break;

      cons = myconss[c];
      assert(cons != NULL);
      assert(SCIPconsIsActive(cons));
      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);
   }
   while( consdata->nvars == nmaxvars );

   /* remove covered constraints and left over constraints to the column representation */
   while( c >= 0 )
   {
      cons = myconss[c];
      assert(cons != NULL);
      assert(SCIPconsIsActive(cons));
      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);

      /* calculate hash-signature */
      consdataCalcSignature(consdata);
      assert(consdata->validsignature);

      /* search for covered constraints */
      if( conschanged || consdata->changed )
      {
         /*  detect covered constraints
          *
          *  e.g.: c1: x1 + x2 + x3 >= 1
          *        c2: x1 + x2 + x3 + x4 >= 1
          *
          *     => delete c2
          */
         SCIP_CALL( removeRedundantConss(scip, cons, varstopos, occurlist, noccurlistentries, occurlistlength, ndelconss) );
         assert(SCIPconsIsActive(cons));

         consdata->changed = FALSE;
         conschanged = TRUE;
      }

      /* add constraint to column data structure */
      SCIP_CALL( addConsToOccurList(scip, cons, varstopos, occurlist, noccurlistentries, occurlistsizes, &occurlistlength, occurlistsize) );

      --c;
   }

   /*  strengthen constraint while removing non-zeros
    *
    *  e.g.: c1: x1 + x2 + x3 >= 1
    *        c2: x1 + x2 + ~x3 + x4 >= 1
    *
    *     => c2: x1 + x2 + x4 >= 1
    *
    *  special case:
    *
    *  e.g.: c1: x1 + x2 + x3 >= 1
    *        c2: x1 + x2 + ~x3 >= 1
    *
    *     => delete c1; c2: x1 + x2 >= 1
    *
    */
   SCIP_CALL( strengthenConss(scip, myconss, nmyconss, varstopos, occurlist, noccurlistentries, occurlistlength, eventhdlr, ndelconss, nchgcoefs) );

   /* delete temporary memory in occurlist */
   for( --occurlistsize ; occurlistsize >= 0; --occurlistsize )
   {
      assert((occurlistsizes[occurlistsize] == 0) == (occurlist[occurlistsize] == NULL));
      SCIPfreeBufferArrayNull(scip, &(occurlist[occurlistsize]));
   }

   /* delete temporary memory */
   SCIPhashmapFree(&varstopos);
   SCIPfreeBufferArray(scip, &occurlistsizes);
   SCIPfreeBufferArray(scip, &noccurlistentries);
   SCIPfreeBufferArray(scip, &occurlist);
   SCIPfreeBufferArray(scip, &myconss);

   return SCIP_OKAY;
}

#define MAX_CONSLENGTH 200

/** try to tighten constraints by reducing the number of variables in the constraints using implications and cliques,
 *  also derive fixations through them, @see SCIPshrinkDisjunctiveVarSet()
 */
static
SCIP_RETCODE shortenConss(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLRDATA*    conshdlrdata,       /**< logic or constraint handler data */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   SCIP_CONS**           conss,              /**< all constraints */
   int                   nconss,             /**< number of constraints */
   unsigned char**       entries,            /**< array to store whether two positions in constraints represent the same
                                              *   variable */
   int*                  nentries,           /**< pointer for array size, if array will be to small it's corrected */
   int*                  nfixedvars,         /**< pointer to count number of fixings */
   int*                  ndelconss,          /**< pointer to count number of deleted constraints */
   int*                  nchgcoefs,          /**< pointer to count number of changed/deleted coefficients */
   SCIP_Bool*            cutoff              /**< pointer to store, if cut off appeared */
   )
{
   SCIP_VAR** probvars;
   SCIP_VAR* var;
   SCIP_Real* bounds;
   SCIP_Bool* boundtypes;
   SCIP_Bool* redundants;
   int nbinprobvars;
   int nredvars;
   int c;
   int v;

   assert(scip != NULL);
   assert(eventhdlr != NULL);
   assert(conss != NULL || nconss == 0);
   assert(entries != NULL);
   assert(*entries != NULL);
   assert(nentries != NULL);
   assert(nfixedvars != NULL);
   assert(ndelconss != NULL);
   assert(nchgcoefs != NULL);

   if( nconss == 0 )
      return SCIP_OKAY;

   assert(conss != NULL);

   if( SCIPgetNCliques(scip) == conshdlrdata->nlastcliquesshorten
      && SCIPgetNImplications(scip) == conshdlrdata->nlastimplsshorten )
      return SCIP_OKAY;

   conshdlrdata->nlastcliquesshorten = SCIPgetNCliques(scip);
   conshdlrdata->nlastimplsshorten = SCIPgetNImplications(scip);

   nbinprobvars = SCIPgetNVars(scip) - SCIPgetNContVars(scip);

   /* allocate temporary memory */
   SCIP_CALL( SCIPallocBufferArray(scip, &probvars, nbinprobvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &bounds, nbinprobvars) );
   SCIP_CALL( SCIPallocBufferArray(scip, &boundtypes, nbinprobvars) );
   SCIP_CALL( SCIPallocCleanBufferArray(scip, &redundants, nbinprobvars) );

   for( c = nconss - 1; c >= 0; --c )
   {
      SCIP_Bool redundant = FALSE;
      SCIP_CONS* cons = conss[c];
      SCIP_CONSDATA* consdata;

      assert(cons != NULL);

      if( SCIPconsIsDeleted(cons) )
         continue;

      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);

      /* prepare constraint by removing fixings and merge it */
      SCIP_CALL( prepareCons(scip, cons, eventhdlr, entries, nentries, &redundant, nfixedvars, nchgcoefs, ndelconss, cutoff) );

      if( redundant )
      {
         assert(SCIPconsIsDeleted(cons));
         continue;
      }

      if( *cutoff )
         goto TERMINATE;

      assert(consdata->nvars >= 2);

      /* do not try to shorten too long constraints */
      if( consdata->nvars > MAX_CONSLENGTH )
         continue;

      /* form necessary data */
      for( v = consdata->nvars - 1; v >= 0; --v)
      {
         var = consdata->vars[v];
         assert(var != NULL);
         assert(SCIPvarIsActive(var) || (SCIPvarGetStatus(var) == SCIP_VARSTATUS_NEGATED && SCIPvarIsActive(SCIPvarGetNegationVar(var))));

         if( SCIPvarIsActive(var) )
         {
            probvars[v] = var;
            bounds[v] = 1.0;
            boundtypes[v] = FALSE;
         }
         else
         {
            probvars[v] = SCIPvarGetNegationVar(var);
            bounds[v] = 0.0;
            boundtypes[v] = TRUE;
         }
      }

      SCIP_CALL( SCIPcleanupCliques(scip, cutoff) );

      if( *cutoff )
         goto TERMINATE;

      /* use implications and cliques to derive global fixings and to shrink the number of variables in this constraints */
      SCIP_CALL( SCIPshrinkDisjunctiveVarSet(scip, probvars, bounds, boundtypes, redundants, consdata->nvars, &nredvars,
            nfixedvars, &redundant, TRUE) );

      /* remove redundant constraint */
      if( redundant )
      {
         SCIP_CALL( SCIPdelCons(scip, cons) );
         ++(*ndelconss);

         /* reset redundants array to FALSE */
#if 1
         BMSclearMemoryArray(redundants, consdata->nvars);
#else
         if( nredvars > 0 )
         {
            for( v = consdata->nvars - 1; v >= 0; --v )
            {
               if( redundants[v] )
               {
                  redundants[v] = FALSE;
               }
            }
         }
#endif
         continue;
      }

      /* remove redundant variables */
      if( nredvars > 0 )
      {
         for( v = consdata->nvars - 1; v >= 0; --v )
         {
            if( redundants[v] )
            {
               SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );

               /* reset entry to FALSE */
               redundants[v] = FALSE;
            }
         }
         *nchgcoefs += nredvars;

         /* if only one variable is left over fix it */
         if( consdata->nvars == 1 )
         {
            SCIP_Bool infeasible;
            SCIP_Bool fixed;

            SCIPdebugMessage(" -> fix last remaining variable and delete constraint\n");

            SCIP_CALL( SCIPfixVar(scip, consdata->vars[0], 1.0, &infeasible, &fixed) );
            assert(!infeasible);
            assert(fixed);
            ++(*nfixedvars);

            SCIP_CALL( SCIPdelCons(scip, cons) );
            ++(*ndelconss);
         }
         /* @todo might also upgrade a two variable constraint to a set-packing constraint */
      }
   }

 TERMINATE:
   /* free temporary memory */
   SCIPfreeCleanBufferArray(scip, &redundants);
   SCIPfreeBufferArray(scip, &boundtypes);
   SCIPfreeBufferArray(scip, &bounds);
   SCIPfreeBufferArray(scip, &probvars);

   return SCIP_OKAY;
}

#define MAXCOMPARISONS 1000000

/** try to find a negated clique in a constraint which makes this constraint redundant but we need to keep the negated
 *  clique information alive, so we create a corresponding set-packing constraint
 */
static
SCIP_RETCODE removeConstraintsDueToNegCliques(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONSHDLR*        conshdlr,           /**< logicor constraint handler */
   SCIP_CONSHDLR*        conshdlrsetppc,     /**< setppc constraint handler, or NULL */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   SCIP_CONS**           conss,              /**< all constraints */
   int                   nconss,             /**< number of constraints */
   unsigned char**       entries,            /**< array to store whether two positions in constraints represent the same
                                              *   variable */
   int*                  nentries,           /**< pointer for array size, if array will be to small it's corrected */
   int*                  nfixedvars,         /**< pointer to count number of fixings */
   int*                  ndelconss,          /**< pointer to count number of deleted constraints */
   int*                  nupgdconss,         /**< pointer to count number of upgraded constraints */
   int*                  nchgcoefs,          /**< pointer to count number of changed/deleted coefficients */
   SCIP_Bool*            cutoff              /**< pointer to store, if cut off appeared */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONS* cons;
   SCIP_CONSDATA* consdata;
   SCIP_VAR** repvars;
   SCIP_Bool* negated;
   SCIP_VAR* var1;
   SCIP_Bool redundant;
   int c;
   int size;
   int maxcomppercons;
   int comppercons;

   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(eventhdlr != NULL);
   assert(conss != NULL || nconss == 0);
   assert(entries != NULL);
   assert(*entries != NULL);
   assert(nentries != NULL);
   assert(nfixedvars != NULL);
   assert(ndelconss != NULL);
   assert(nupgdconss != NULL);
   assert(nchgcoefs != NULL);
   assert(cutoff != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   if( nconss == 0 )
      return SCIP_OKAY;

   if( SCIPgetNCliques(scip) == conshdlrdata->nlastcliquesneg && SCIPgetNImplications(scip) == conshdlrdata->nlastimplsneg )
      return SCIP_OKAY;

   conshdlrdata->nlastcliquesneg = SCIPgetNCliques(scip);
   conshdlrdata->nlastimplsneg = SCIPgetNImplications(scip);

   /* estimate the maximal number of variables in a logicor constraint */
   size = SCIPgetNVars(scip) - SCIPgetNContVars(scip);
   if( size <= 0 )
      return SCIP_OKAY;

   /* temporary memory for active/negation of active variables */
   SCIP_CALL( SCIPallocBufferArray(scip, &repvars, size) );
   SCIP_CALL( SCIPallocBufferArray(scip, &negated, size) );

   /* iterate over all constraints and try to find negated cliques in logicors */
   for( c = nconss - 1; c >= 0; --c )
   {
      int v;

      assert(conss != NULL); /* for flexelint */

      cons = conss[c];
      assert(cons != NULL);

      if( !SCIPconsIsActive(cons) )
         continue;

      /* prepare constraint by removing fixings and merge it */
      SCIP_CALL( prepareCons(scip, cons, eventhdlr, entries, nentries, &redundant, nfixedvars, nchgcoefs, ndelconss, cutoff) );

      if( redundant )
      {
         assert(SCIPconsIsDeleted(cons));
         continue;
      }

      if( *cutoff )
         goto TERMINATE;

      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);
      assert(consdata->nvars >= 2);
      assert(consdata->nvars <= size);
      assert(consdata->presolved);

      if( SCIPconsIsModifiable(cons) && consdata->nvars == 2 )
         continue;

      if( c % 100 == 0 && SCIPisStopped(scip) )
         break;

      maxcomppercons = MAXCOMPARISONS / nconss;
      comppercons = 0;

      BMScopyMemoryArray(repvars, consdata->vars, consdata->nvars);

      /* all variables should be active or negative active variables, otherwise something went wrong with applyFixings()
       * called before mergeMultiples()
       */
      for( v = consdata->nvars - 1; v >= 0; --v )
      {
         assert(SCIPvarIsActive(repvars[v]) || (SCIPvarGetStatus(repvars[v]) == SCIP_VARSTATUS_NEGATED && SCIPvarIsActive(SCIPvarGetNegationVar(repvars[v]))));
         negated[v] = SCIPvarIsNegated(repvars[v]);
      }

      for( v = consdata->nvars - 1; v > 0; --v )
      {
         SCIP_Bool breakloop;
         SCIP_Bool neg1;
         int w;

         var1 = repvars[v];
         neg1 = negated[v];

         /* if there is no negated variable, there can't be a negated clique */
         if( SCIPvarGetNegatedVar(var1) == NULL )
            continue;

         /* get active counterpart to check for common cliques */
         if( SCIPvarGetStatus(var1) == SCIP_VARSTATUS_NEGATED )
         {
            var1 = SCIPvarGetNegatedVar(var1);
            neg1 = TRUE;
         }
         else
            neg1 = FALSE;

         if( !SCIPvarIsActive(var1) )
            continue;

         /* no cliques available */
         if( SCIPvarGetNCliques(var1, neg1) == 0 && SCIPvarGetNImpls(var1, neg1) == 0 )
            continue;

         comppercons += (v - 1);

         breakloop = FALSE;

         for( w = v - 1; w >= 0; --w )
         {
            SCIP_VAR* var2;
            SCIP_Bool neg2;

            var2 = repvars[w];
            neg2 = negated[w];

            /* if there is no negated variable, there can't be a negated clique */
            if( SCIPvarGetNegatedVar(var2) == NULL )
               continue;

            if( SCIPvarGetStatus(var2) == SCIP_VARSTATUS_NEGATED )
            {
               var2 = SCIPvarGetNegatedVar(var2);
               neg2 = TRUE;
            }
            else
               neg2 = FALSE;

            if( !SCIPvarIsActive(var2) )
               continue;

            /* no cliques available */
            if( SCIPvarGetNCliques(var2, neg2) == 0 && SCIPvarGetNImpls(var2, neg2) == 0 )
               continue;

            /* check if both active variable are the same */
            if( var1 == var2 )
            {
               if( neg1 != neg2 )
               {
                  SCIPdebugMessage("logicor constraint <%s> is redundant, because variable <%s> and its negation <%s> exist\n", SCIPconsGetName(cons), SCIPvarGetName(var1), SCIPvarGetName(var2));

                  SCIP_CALL( SCIPdelCons(scip, cons) );

                  breakloop = TRUE;
               }
               else
               {
#ifndef NDEBUG
                  SCIP_VAR* lastvar = consdata->vars[consdata->nvars - 1];
#endif
                  SCIPdebugMessage("in logicor constraint <%s>, active variable of <%s> and active variable of <%s> are the same, removing the first\n", SCIPconsGetName(cons), SCIPvarGetName(consdata->vars[v]), SCIPvarGetName(consdata->vars[w]));

                  SCIP_CALL( delCoefPos(scip, cons, eventhdlr, v) );

                  if( v < consdata->nvars )
                  {
                     /* delCoefPos replaces the variable on position v with the last one, so w also need to correct the
                      * negated array the same way, and because of deletion the number of variables is already decreased
                      */
                     assert(consdata->vars[v] == lastvar);
                     negated[v] = negated[consdata->nvars];
                  }
                  ++(*nchgcoefs);
               }
               break;
            }

            if( SCIPvarsHaveCommonClique(var1, neg1, var2, neg2, TRUE) && conshdlrsetppc != NULL )
            {
               SCIP_CONS* newcons;
               SCIP_VAR* vars[2];

               /* this negated clique information could be created out of this logicor constraint even if there are more
                * than two variables left (, for example by probing), we need to keep this information by creating a
                * setppc constraint instead 
                */

               /* get correct variables */
               if( !neg1 )
                  vars[0] = SCIPvarGetNegatedVar(var1);
               else
                  vars[0] = var1;

               if( !neg2 )
                  vars[1] = SCIPvarGetNegatedVar(var2);
               else
                  vars[1] = var2;

               SCIP_CALL( SCIPcreateConsSetpack(scip, &newcons, SCIPconsGetName(cons), 2, vars, 
                     SCIPconsIsInitial(cons), SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons), 
                     SCIPconsIsChecked(cons), SCIPconsIsPropagated(cons),
                     SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons), 
                     SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );

               SCIP_CALL( SCIPaddCons(scip, newcons) );
               SCIPdebugPrintCons(scip, newcons, NULL);

               SCIP_CALL( SCIPreleaseCons(scip, &newcons) );

               SCIPdebugMessage("logicor constraint <%s> is redundant due to negated clique information and will be replaced by a setppc constraint \n", SCIPconsGetName(cons));
               SCIPdebugMessage("variable <%s> and variable <%s> are in a negated clique\n", SCIPvarGetName(consdata->vars[v]), SCIPvarGetName(consdata->vars[w]));

               SCIP_CALL( SCIPdelCons(scip, cons) );
               ++(*nupgdconss);

               breakloop = TRUE;
               break;
            }
         }
         if( breakloop )
            break;

         /* do not do to many comparisons */
         if( comppercons > maxcomppercons )
            break;
      }
   }

 TERMINATE:
   /* free temporary memory */
   SCIPfreeBufferArray(scip, &negated);
   SCIPfreeBufferArray(scip, &repvars);

   return SCIP_OKAY;
}

/** handle all cases with less than three variables in a logicor constraint
 *
 *  in case a constraint has zero variables left, we detected infeasibility
 *  in case a constraint has one variables left, we will fix it to one
 *  in case a constraint has two variables left, we will add the implication and upgrade it to a set-packing constraint
 */
static
SCIP_RETCODE fixDeleteOrUpgradeCons(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logic or constraint */
   SCIP_EVENTHDLR*       eventhdlr,          /**< event handler to call for the event processing */
   SCIP_CONSHDLR*        conshdlrlinear,     /**< linear constraint handler, or NULL */
   SCIP_CONSHDLR*        conshdlrsetppc,     /**< setppc constraint handler, or NULL */
   int*                  nfixedvars,         /**< pointer to count number of fixings */
   int*                  nchgbds,            /**< pointer to count number of tightened bounds */
   int*                  nchgcoefs,          /**< pointer to count number of changed/deleted coefficients */
   int*                  ndelconss,          /**< pointer to count number of deleted constraints  */
   int*                  naddconss,          /**< pointer to count number of added constraints */
   int*                  nupgdconss,         /**< pointer to count number of upgraded constraints */
   SCIP_Bool*            cutoff              /**< pointer to store TRUE, if the node can be cut off */
   )
{
   SCIP_CONSDATA* consdata;
   SCIP_Bool infeasible;
   SCIP_Bool fixed;

   assert(scip != NULL);
   assert(cons != NULL);
   assert(eventhdlr != NULL);
   assert(nfixedvars != NULL);
   assert(nchgbds != NULL);
   assert(nchgcoefs != NULL);
   assert(ndelconss != NULL);
   assert(naddconss != NULL);
   assert(nupgdconss != NULL);
   assert(cutoff != NULL);

   *cutoff = FALSE;

   if( SCIPconsIsModifiable(cons) )
      return SCIP_OKAY;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* if an unmodifiable logicor constraint has only two variables, we can add an implication and we will upgrade this
    * constraint to a set-packing constraint
    */
   if( consdata->nvars == 2 )
   {
      /* add implication if not yet done */
      if( !consdata->impladded )
      {
         SCIP_Bool implinfeasible;
         int nimplbdchgs;
         SCIP_Bool values[2];

         values[0] = FALSE;
         values[1] = FALSE;
         /* a two-variable logicor constraint x + y >= 1 yields the implication x == 0 -> y == 1, and is represented
          * by the clique inequality ~x + ~y <= 1
          */
         SCIP_CALL( SCIPaddClique(scip, consdata->vars, values, consdata->nvars, FALSE, &implinfeasible, &nimplbdchgs) );
         *nchgbds += nimplbdchgs;
         if( implinfeasible )
         {
            *cutoff = TRUE;
            return SCIP_OKAY;
         }

         /* adding the above implication could lead to fixings, which render the constraint redundant */
         if ( nimplbdchgs > 0 )
         {
            SCIP_Bool redundant;

            /* remove all variables that are fixed to zero, check redundancy due to fixed-to-one variable */
            SCIP_CALL( applyFixings(scip, cons, eventhdlr, &redundant, nchgcoefs, naddconss, ndelconss) );
            assert(!SCIPconsIsDeleted(cons));

            if( redundant )
            {
               SCIPdebugMessage("logic or constraint <%s> is redundant\n", SCIPconsGetName(cons));

               SCIP_CALL( SCIPdelCons(scip, cons) );
               (*ndelconss)++;

               return SCIP_OKAY;
            }
         }
         consdata->impladded = TRUE;
      }

      /* still we have two variables left, we will upgrade this constraint */
      if( consdata->nvars == 2 && conshdlrsetppc != NULL )
      {
         SCIP_CONS* newcons;
         SCIP_VAR* vars[2];


         /* get correct variables */
         SCIP_CALL( SCIPgetNegatedVar(scip, consdata->vars[0], &vars[0]) );
         SCIP_CALL( SCIPgetNegatedVar(scip, consdata->vars[1], &vars[1]) );

         SCIP_CALL( SCIPcreateConsSetpack(scip, &newcons, SCIPconsGetName(cons), 2, vars,
               SCIPconsIsInitial(cons), SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons),
               SCIPconsIsChecked(cons), SCIPconsIsPropagated(cons),
               SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
               SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );

         SCIP_CALL( SCIPaddCons(scip, newcons) );
         SCIPdebugPrintCons(scip, newcons, NULL);

         SCIP_CALL( SCIPreleaseCons(scip, &newcons) );

         SCIPdebugMessage("logicor constraint <%s> was upgraded to a set-packing constraint\n", SCIPconsGetName(cons));

         SCIP_CALL( SCIPdelCons(scip, cons) );
         ++(*nupgdconss);
      }
   }

   /* if unmodifiable constraint has no variables, it is infeasible,
    * if unmodifiable constraint has only one variable, this one can be fixed and the constraint deleted
    */
   if( consdata->nvars == 0 )
   {
      SCIPdebugMessage("logic or constraint <%s> is infeasible\n", SCIPconsGetName(cons));

      *cutoff = TRUE;
   }
   else if( consdata->nvars == 1 )
   {
      SCIPdebugMessage("logic or constraint <%s> has only one variable not fixed to 0.0\n",
         SCIPconsGetName(cons));

      assert(consdata->vars != NULL);
      assert(consdata->vars[0] != NULL);

      if( SCIPvarGetStatus(consdata->vars[0]) != SCIP_VARSTATUS_MULTAGGR )
      {
         SCIPdebugMessage(" -> fix variable and delete constraint\n");

         SCIP_CALL( SCIPfixVar(scip, consdata->vars[0], 1.0, &infeasible, &fixed) );
         if( infeasible )
         {
            SCIPdebugMessage(" -> infeasible fixing\n");

            *cutoff = TRUE;
            return SCIP_OKAY;
         }
         if( fixed )
            (*nfixedvars)++;

         SCIP_CALL( SCIPdelCons(scip, cons) );
         (*ndelconss)++;
      }
      else if( conshdlrlinear != NULL )
      {
         SCIP_Real coef;
         SCIP_CONS* conslinear;
         char consname[SCIP_MAXSTRLEN];

         SCIPdebugMessage(" -> variable is multi-aggregated, upgrade to linear constraint <%s> == 1 \n",
            SCIPvarGetName(consdata->vars[0]));

         coef = 1.0;
         (void) SCIPsnprintf(consname, SCIP_MAXSTRLEN, "fixmaggr_%s_%s", SCIPconsGetName(cons),SCIPvarGetName(consdata->vars[0]) );
         SCIP_CALL( SCIPcreateConsLinear(scip, &conslinear, consname, 1, consdata->vars, &coef, 1.0, 1.0,
               SCIPconsIsInitial(cons), SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons),
               SCIPconsIsChecked(cons), SCIPconsIsPropagated(cons), SCIPconsIsLocal(cons),
               SCIPconsIsModifiable(cons), SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons),
               SCIPconsIsStickingAtNode(cons)) );

         /* add constraint */
         SCIP_CALL( SCIPaddCons(scip, conslinear) );
         SCIP_CALL( SCIPreleaseCons(scip, &conslinear) );
         SCIP_CALL( SCIPdelCons(scip, cons) );

         (*ndelconss)++;
         (*naddconss)++;
      }
   }

   return SCIP_OKAY;
}


/*
 * upgrading of linear constraints
 */

/** creates and captures a normalized (with all coefficients +1) logic or constraint */
static
SCIP_RETCODE createNormalizedLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nvars,              /**< number of variables in the constraint */
   SCIP_VAR**            vars,               /**< array with variables of constraint entries */
   SCIP_Real*            vals,               /**< array with coefficients (+1.0 or -1.0) */
   int                   mult,               /**< multiplier on the coefficients(+1 or -1) */
   SCIP_Bool             initial,            /**< should the LP relaxation of constraint be in the initial LP? 
                                              *   Usually set to TRUE. Set to FALSE for 'lazy constraints'. */
   SCIP_Bool             separate,           /**< should the constraint be separated during LP processing? 
                                              *   Usually set to TRUE. */
   SCIP_Bool             enforce,            /**< should the constraint be enforced during node processing? 
                                              *   TRUE for model constraints, FALSE for additional, redundant constraints. */
   SCIP_Bool             check,              /**< should the constraint be checked for feasibility? 
                                              *   TRUE for model constraints, FALSE for additional, redundant constraints. */
   SCIP_Bool             propagate,          /**< should the constraint be propagated during node processing? 
                                              *   Usually set to TRUE. */
   SCIP_Bool             local,              /**< is constraint only valid locally? 
                                              *   Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints. */
   SCIP_Bool             modifiable,         /**< is constraint modifiable (subject to column generation)? 
                                              *   Usually set to FALSE. In column generation applications, set to TRUE if pricing
                                              *   adds coefficients to this constraint. */
   SCIP_Bool             dynamic,            /**< is constraint subject to aging? 
                                              *   Usually set to FALSE. Set to TRUE for own cuts which 
                                              *   are separated as constraints. */
   SCIP_Bool             removable,          /**< should the relaxation be removed from the LP due to aging or cleanup? 
                                              *   Usually set to FALSE. Set to TRUE for 'lazy constraints' and 'user cuts'. */
   SCIP_Bool             stickingatnode      /**< should the constraint always be kept at the node where it was added, even
                                              *   if it may be moved to a more global node? 
                                              *   Usually set to FALSE. Set to TRUE to for constraints that represent node data. */
   )
{
   SCIP_VAR** transvars;
   int v;

   assert(nvars == 0 || vars != NULL);
   assert(nvars == 0 || vals != NULL);
   assert(mult == +1 || mult == -1);

   /* get temporary memory */
   SCIP_CALL( SCIPallocBufferArray(scip, &transvars, nvars) );

   /* negate positive or negative variables */
   for( v = 0; v < nvars; ++v )
   {
      if( mult * vals[v] > 0.0 )
         transvars[v] = vars[v];
      else
      {
         SCIP_CALL( SCIPgetNegatedVar(scip, vars[v], &transvars[v]) );
      }
      assert(transvars[v] != NULL);
   }

   /* create the constraint */
   SCIP_CALL( SCIPcreateConsLogicor(scip, cons, name, nvars, transvars,
         initial, separate, enforce, check, propagate, local, modifiable, dynamic, removable, stickingatnode) );

   /* free temporary memory */
   SCIPfreeBufferArray(scip, &transvars);

   return SCIP_OKAY;
}

static
SCIP_DECL_LINCONSUPGD(linconsUpgdLogicor)
{  /*lint --e{715}*/
   assert(upgdcons != NULL);

   /* check, if linear constraint can be upgraded to logic or constraint
    * - logic or constraints consist only of binary variables with a
    *   coefficient of +1.0 or -1.0 (variables with -1.0 coefficients can be negated):
    *        lhs     <= x1 + ... + xp - y1 - ... - yn <= rhs
    * - negating all variables y = (1-Y) with negative coefficients gives:
    *        lhs + n <= x1 + ... + xp + Y1 + ... + Yn <= rhs + n
    * - negating all variables x = (1-X) with positive coefficients and multiplying with -1 gives:
    *        p - rhs <= X1 + ... + Xp + y1 + ... + yn <= p - lhs
    * - logic or constraints have left hand side of +1.0, and right hand side of +infinity: x(S) >= 1.0
    *    -> without negations:  (lhs == 1 - n  and  rhs == +inf)  or  (lhs == -inf  and  rhs = p - 1)
    */
   if( nvars > 2 && nposbin + nnegbin + nposimplbin + nnegimplbin == nvars && ncoeffspone + ncoeffsnone == nvars
      && ((SCIPisEQ(scip, lhs, 1.0 - ncoeffsnone) && SCIPisInfinity(scip, rhs))
         || (SCIPisInfinity(scip, -lhs) && SCIPisEQ(scip, rhs, ncoeffspone - 1.0))) )
   {
      int mult;

      SCIPdebugMessage("upgrading constraint <%s> to logic or constraint\n", SCIPconsGetName(cons));

      /* check, if we have to multiply with -1 (negate the positive vars) or with +1 (negate the negative vars) */
      mult = SCIPisInfinity(scip, rhs) ? +1 : -1;

      /* create the logic or constraint (an automatically upgraded constraint is always unmodifiable) */
      assert(!SCIPconsIsModifiable(cons));
      SCIP_CALL( createNormalizedLogicor(scip, upgdcons, SCIPconsGetName(cons), nvars, vars, vals, mult,
            SCIPconsIsInitial(cons), SCIPconsIsSeparated(cons), SCIPconsIsEnforced(cons),
            SCIPconsIsChecked(cons), SCIPconsIsPropagated(cons),
            SCIPconsIsLocal(cons), SCIPconsIsModifiable(cons),
            SCIPconsIsDynamic(cons), SCIPconsIsRemovable(cons), SCIPconsIsStickingAtNode(cons)) );
   }

   return SCIP_OKAY;
}


/*
 * Callback methods of constraint handler
 */

/** copy method for constraint handler plugins (called when SCIP copies plugins) */
static
SCIP_DECL_CONSHDLRCOPY(conshdlrCopyLogicor)
{  /*lint --e{715}*/
   assert(scip != NULL);
   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);

   /* call inclusion method of constraint handler */
   SCIP_CALL( SCIPincludeConshdlrLogicor(scip) );

   *valid = TRUE;

   return SCIP_OKAY;
}

/** destructor of constraint handler to free constraint handler data (called when SCIP is exiting) */
static
SCIP_DECL_CONSFREE(consFreeLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(scip != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   /* free constraint handler data */
   SCIP_CALL( conshdlrdataFree(scip, &conshdlrdata) );

   SCIPconshdlrSetData(conshdlr, NULL);

   return SCIP_OKAY;
}


/** presolving initialization method of constraint handler (called when presolving is about to begin) */
static
SCIP_DECL_CONSINITPRE(consInitpreLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   int c;
   int v;

   assert(conshdlr != NULL);
   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   conshdlrdata->nlastcliquesneg = 0;
   conshdlrdata->nlastimplsneg = 0;
   conshdlrdata->nlastcliquesshorten = 0;
   conshdlrdata->nlastimplsshorten = 0;

   /* catch all variable event for deleted variables, which is only used in presolving */
   for( c = nconss - 1; c >= 0; --c )
   {
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      for( v = consdata->nvars - 1; v >= 0; --v )
      {
         SCIP_CALL( SCIPcatchVarEvent(scip, consdata->vars[v], SCIP_EVENTTYPE_VARFIXED, conshdlrdata->eventhdlr,
               (SCIP_EVENTDATA*)conss[c], NULL) );
      }
   }

   return SCIP_OKAY;
}
/** presolving deinitialization method of constraint handler (called after presolving has been finished) */
static
SCIP_DECL_CONSEXITPRE(consExitpreLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;
   SCIP_Bool redundant;
   int nchgcoefs = 0;
   int c;
   int v;

   assert(conshdlr != NULL);
   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   /* drop all variable event for deleted variables, which was only used in presolving */
   for( c = 0; c < nconss; ++c )
   {
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      for( v = 0; v < consdata->nvars; ++v )
      {
         SCIP_CALL( SCIPdropVarEvent(scip, consdata->vars[v], SCIP_EVENTTYPE_VARFIXED, conshdlrdata->eventhdlr,
               (SCIP_EVENTDATA*)conss[c], -1) );
      }

      if( !SCIPconsIsDeleted(conss[c]) && !consdata->presolved )
      {
         /* we are not allowed to detect infeasibility in the exitpre stage */
         SCIP_CALL( applyFixings(scip, conss[c], conshdlrdata->eventhdlr, &redundant, &nchgcoefs, NULL, NULL) );
      }
   }

   return SCIP_OKAY;
}


/** solving process deinitialization method of constraint handler (called before branch and bound process data is freed) */
static
SCIP_DECL_CONSEXITSOL(consExitsolLogicor)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;
   int c;

   /* release the rows of all constraints */
   for( c = 0; c < nconss; ++c )
   {
      consdata = SCIPconsGetData(conss[c]);
      assert(consdata != NULL);

      if( consdata->row != NULL )
      {
         SCIP_CALL( SCIPreleaseRow(scip, &consdata->row) );
      }
   }

   return SCIP_OKAY;
}


/** frees specific constraint data */
static
SCIP_DECL_CONSDELETE(consDeleteLogicor)
{  /*lint --e{715}*/
   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(consdata != NULL);
   assert(*consdata != NULL);

   if( SCIPgetStage(scip) == SCIP_STAGE_PRESOLVING || SCIPgetStage(scip) == SCIP_STAGE_INITPRESOLVE )
   {
      SCIP_CONSHDLRDATA* conshdlrdata;
      int v;

      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);

      for( v = (*consdata)->nvars - 1; v >= 0; --v )
      {
         SCIP_CALL( SCIPdropVarEvent(scip, (*consdata)->vars[v], SCIP_EVENTTYPE_VARFIXED, conshdlrdata->eventhdlr,
               (SCIP_EVENTDATA*)cons, -1) );
      }
   }

   /* free LP row and logic or constraint */
   SCIP_CALL( consdataFree(scip, consdata) );

   return SCIP_OKAY;
}


/** transforms constraint data into data belonging to the transformed problem */ 
static
SCIP_DECL_CONSTRANS(consTransLogicor)
{  /*lint --e{715}*/
   SCIP_CONSDATA* sourcedata;
   SCIP_CONSDATA* targetdata;

   /*debugMessage("Trans method of logic or constraints\n");*/

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(SCIPgetStage(scip) == SCIP_STAGE_TRANSFORMING);
   assert(sourcecons != NULL);
   assert(targetcons != NULL);

   sourcedata = SCIPconsGetData(sourcecons);
   assert(sourcedata != NULL);
   assert(sourcedata->row == NULL);  /* in original problem, there cannot be LP rows */

   /* create constraint data for target constraint */
   SCIP_CALL( consdataCreate(scip, &targetdata, sourcedata->nvars, sourcedata->vars) );

   /* create target constraint */
   SCIP_CALL( SCIPcreateCons(scip, targetcons, SCIPconsGetName(sourcecons), conshdlr, targetdata,
         SCIPconsIsInitial(sourcecons), SCIPconsIsSeparated(sourcecons), SCIPconsIsEnforced(sourcecons),
         SCIPconsIsChecked(sourcecons), SCIPconsIsPropagated(sourcecons),
         SCIPconsIsLocal(sourcecons), SCIPconsIsModifiable(sourcecons), 
         SCIPconsIsDynamic(sourcecons), SCIPconsIsRemovable(sourcecons), SCIPconsIsStickingAtNode(sourcecons)) );

   return SCIP_OKAY;
}


/** LP initialization method of constraint handler (called before the initial LP relaxation at a node is solved) */
static
SCIP_DECL_CONSINITLP(consInitlpLogicor)
{  /*lint --e{715}*/
   SCIP_Bool cutoff = FALSE;
   int c;

   for( c = 0; c < nconss; ++c )
   {
      assert(SCIPconsIsInitial(conss[c]));
      SCIP_CALL( addCut(scip, conss[c], NULL, &cutoff) );
      /* ignore cutoff, cannot return value */
   }

   return SCIP_OKAY;
}


/** separation method of constraint handler for LP solutions */
static
SCIP_DECL_CONSSEPALP(consSepalpLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_Bool cutoff;
   SCIP_Bool separated;
   SCIP_Bool reduceddom;
   int c;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(nconss == 0 || conss != NULL);
   assert(result != NULL);

   SCIPdebugMessage("separating %d/%d logic or constraints\n", nusefulconss, nconss);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   cutoff = FALSE;
   separated = FALSE;
   reduceddom = FALSE;

   /* check all useful logic or constraints for feasibility */
   for( c = 0; c < nusefulconss && !cutoff; ++c )
   {
      SCIP_CALL( separateCons(scip, conss[c], NULL, conshdlrdata->eventhdlr, &cutoff, &separated, &reduceddom) );
   }

   /* combine logic or constraints to get more cuts */
   /**@todo further cuts of logic or constraints */

   /* return the correct result */
   if( cutoff )
      *result = SCIP_CUTOFF;
   else if( reduceddom )
      *result = SCIP_REDUCEDDOM;
   else if( separated )
      *result = SCIP_SEPARATED;
   else
      *result = SCIP_DIDNOTFIND;

   return SCIP_OKAY;
}


/** separation method of constraint handler for arbitrary primal solutions */
static
SCIP_DECL_CONSSEPASOL(consSepasolLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_Bool cutoff;
   SCIP_Bool separated;
   SCIP_Bool reduceddom;
   int c;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(nconss == 0 || conss != NULL);
   assert(result != NULL);

   SCIPdebugMessage("separating %d/%d logic or constraints\n", nusefulconss, nconss);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   cutoff = FALSE;
   separated = FALSE;
   reduceddom = FALSE;

   /* check all useful logic or constraints for feasibility */
   for( c = 0; c < nusefulconss && !cutoff; ++c )
   {
      SCIP_CALL( separateCons(scip, conss[c], sol, conshdlrdata->eventhdlr, &cutoff, &separated, &reduceddom) );
   }

   /* combine logic or constraints to get more cuts */
   /**@todo further cuts of logic or constraints */

   /* return the correct result */
   if( cutoff )
      *result = SCIP_CUTOFF;
   else if( reduceddom )
      *result = SCIP_REDUCEDDOM;
   else if( separated )
      *result = SCIP_SEPARATED;
   else
      *result = SCIP_DIDNOTFIND;

   return SCIP_OKAY;
}


/** constraint enforcing method of constraint handler for LP solutions */
static
SCIP_DECL_CONSENFOLP(consEnfolpLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_Bool cutoff;
   SCIP_Bool separated;
   SCIP_Bool reduceddom;
   int c;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(nconss == 0 || conss != NULL);
   assert(result != NULL);

   SCIPdebugMessage("LP enforcing %d logic or constraints\n", nconss);

   *result = SCIP_FEASIBLE;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   cutoff = FALSE;
   separated = FALSE;
   reduceddom = FALSE;

   /* check all useful logic or constraints for feasibility */
   for( c = 0; c < nusefulconss && !cutoff && !reduceddom; ++c )
   {
      SCIP_CALL( separateCons(scip, conss[c], NULL, conshdlrdata->eventhdlr, &cutoff, &separated, &reduceddom) );
   }

   /* check all obsolete logic or constraints for feasibility */
   for( c = nusefulconss; c < nconss && !cutoff && !separated && !reduceddom; ++c )
   {
      SCIP_CALL( separateCons(scip, conss[c], NULL, conshdlrdata->eventhdlr, &cutoff, &separated, &reduceddom) );
   }

   /* return the correct result */
   if( cutoff )
      *result = SCIP_CUTOFF;
   else if( separated )
      *result = SCIP_SEPARATED;
   else if( reduceddom )
      *result = SCIP_REDUCEDDOM;

   return SCIP_OKAY;
}


/** constraint enforcing method of constraint handler for pseudo solutions */
static
SCIP_DECL_CONSENFOPS(consEnfopsLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_Bool cutoff;
   SCIP_Bool infeasible;
   SCIP_Bool reduceddom;
   SCIP_Bool solvelp;
   int c;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(nconss == 0 || conss != NULL);
   assert(result != NULL);

   SCIPdebugMessage("pseudo enforcing %d logic or constraints\n", nconss);

   *result = SCIP_FEASIBLE;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   cutoff = FALSE;
   infeasible = FALSE;
   reduceddom = FALSE;
   solvelp = FALSE;

   /* check all logic or constraints for feasibility */
   for( c = 0; c < nconss && !cutoff && !reduceddom && !solvelp; ++c )
   {
      SCIP_CALL( enforcePseudo(scip, conss[c], conshdlrdata->eventhdlr, &cutoff, &infeasible, &reduceddom, &solvelp) );
   }

   if( cutoff )
      *result = SCIP_CUTOFF;
   else if( reduceddom )
      *result = SCIP_REDUCEDDOM;
   else if( solvelp )
      *result = SCIP_SOLVELP;
   else if( infeasible )
      *result = SCIP_INFEASIBLE;

   return SCIP_OKAY;
}


/** feasibility check method of constraint handler for integral solutions */
static
SCIP_DECL_CONSCHECK(consCheckLogicor)
{  /*lint --e{715}*/
   SCIP_CONS* cons;
   SCIP_CONSDATA* consdata;
   int c;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(nconss == 0 || conss != NULL);
   assert(result != NULL);

   *result = SCIP_FEASIBLE;

   /* check all logic or constraints for feasibility */
   for( c = 0; c < nconss; ++c )
   {
      cons = conss[c];
      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);
      if( checklprows || consdata->row == NULL || !SCIProwIsInLP(consdata->row) )
      {
         SCIP_Bool violated;

         SCIP_CALL( checkCons(scip, cons, sol, &violated) );
         if( violated )
         {
            /* constraint is violated */
            *result = SCIP_INFEASIBLE;

            if( printreason )
            {
#ifndef NDEBUG
               int v;
               for( v = 0; v < consdata->nvars; ++v )
               {
                  assert( consdata->vars[v] != NULL);
                  assert( SCIPvarIsBinary(consdata->vars[v]) );
                  assert( SCIPisFeasLT(scip, SCIPgetSolVal(scip, sol, consdata->vars[v]), 1.0) );
               }
#endif
               SCIP_CALL( SCIPprintCons(scip, cons, NULL) );
               SCIPinfoMessage(scip, NULL, ";\n");
               SCIPinfoMessage(scip, NULL, "violation: all variables are set to zero\n");
            }

            return SCIP_OKAY;
         }
      }
   }

   return SCIP_OKAY;
}


/** domain propagation method of constraint handler */
static
SCIP_DECL_CONSPROP(consPropLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_Bool cutoff;
   SCIP_Bool reduceddom;
   SCIP_Bool addcut;
   SCIP_Bool mustcheck;
   int c;
#ifndef NDEBUG
   SCIP_Bool inpresolve = (SCIPgetStage(scip) < SCIP_STAGE_INITSOLVE);
#endif

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(nconss == 0 || conss != NULL);
   assert(result != NULL);

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   cutoff = FALSE;
   reduceddom = FALSE;

   /* propagate all useful logic or constraints */
   for( c = 0; c < nusefulconss && !cutoff; ++c )
   {
      assert(inpresolve || !(SCIPconsGetData(conss[c])->existmultaggr));

      SCIPdebugMessage(" propagate constraint %s\n", SCIPconsGetName(conss[c]));
      SCIP_CALL( processWatchedVars(scip, conss[c], conshdlrdata->eventhdlr, &cutoff, &reduceddom, &addcut, &mustcheck) );
   }

   /* return the correct result */
   if( cutoff )
      *result = SCIP_CUTOFF;
   else if( reduceddom )
      *result = SCIP_REDUCEDDOM;
   else
      *result = SCIP_DIDNOTFIND;

   return SCIP_OKAY;
}

/** presolving method of constraint handler */
static
SCIP_DECL_CONSPRESOL(consPresolLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONS* cons;
   SCIP_CONSDATA* consdata;
   unsigned char* entries;
   SCIP_Bool redundant;
   int c;
   int firstchange;
   int nentries;
   int oldnfixedvars;
   int oldnchgbds;
   int oldndelconss;
   int oldnupgdconss;
   int oldnchgcoefs;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(scip != NULL);
   assert(result != NULL);

   *result = SCIP_DIDNOTFIND;

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);

   nentries = SCIPgetNVars(scip) - SCIPgetNContVars(scip);

   oldnfixedvars = *nfixedvars;
   oldnchgbds = *nchgbds;
   oldndelconss = *ndelconss;
   oldnupgdconss = *nupgdconss;
   oldnchgcoefs = *nchgcoefs;

   firstchange = INT_MAX;

   SCIP_CALL( SCIPallocBufferArray(scip, &entries, nentries) );

   /* process constraints */
   for( c = 0; c < nconss && *result != SCIP_CUTOFF && !SCIPisStopped(scip); ++c )
   {
      cons = conss[c];
      assert(cons != NULL);
      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);

      SCIPdebugMessage("presolving logic or constraint <%s>\n", SCIPconsGetName(cons));

      /* force presolving the constraint in the initial round */
      if( nrounds == 0 )
      {
         SCIP_CALL( SCIPenableConsPropagation(scip, cons) );
      }

      redundant = FALSE;
      if( !consdata->presolved )
      {
         /* remove all variables that are fixed to zero, check redundancy due to fixed-to-one variable */
         SCIP_CALL( applyFixings(scip, cons, conshdlrdata->eventhdlr, &redundant, nchgcoefs, naddconss, ndelconss) );
      }

      if( SCIPconsIsDeleted(cons) )
         continue;

      /* find pairs of negated variables in constraint: constraint is redundant */
      /* find sets of equal variables in constraint: multiple entries of variable can be replaced by single entry */
      if( !redundant )
      {
         SCIP_CALL( mergeMultiples(scip, cons, conshdlrdata->eventhdlr, &entries, &nentries, &redundant, nchgcoefs) );
      }

      if( redundant )
      {
         SCIPdebugMessage("logic or constraint <%s> is redundant\n", SCIPconsGetName(cons));
         SCIP_CALL( SCIPdelCons(scip, cons) );
         (*ndelconss)++;
         *result = SCIP_SUCCESS;
         continue;
      }
      else if( !SCIPconsIsModifiable(cons) )
      {
         if( consdata->nvars <= 2 )
         {
            SCIP_Bool cutoff;

            /* handle all cases with less than three variables in a logicor constraint */
            SCIP_CALL( fixDeleteOrUpgradeCons(scip, cons, conshdlrdata->eventhdlr, conshdlrdata->conshdlrlinear,
                  conshdlrdata->conshdlrsetppc, nfixedvars, nchgbds, nchgcoefs, ndelconss, naddconss, nupgdconss, &cutoff) );

            if( cutoff )
            {
               *result = SCIP_CUTOFF;
               goto TERMINATE;
            }
            else if( *nfixedvars > oldnfixedvars || *nchgbds > oldnchgbds || *nchgcoefs > oldnchgcoefs
               || *ndelconss > oldndelconss  || *nupgdconss > oldnupgdconss )
               *result = SCIP_SUCCESS;

            if( SCIPconsIsDeleted(cons) )
               continue;
         }
      }

      /* perform dual reductions */
      if( conshdlrdata->dualpresolving && SCIPallowDualReds(scip) )
      {
         SCIP_CALL( dualPresolving(scip, cons, conshdlrdata->eventhdlr, nfixedvars, ndelconss, nchgcoefs, result) );

         /* if dual reduction deleted the constraint we take the next */
         if( !SCIPconsIsActive(cons) )
            continue;

         /* in dualpresolving we may have removed variables, so we need to take care of special cases */
         if( consdata->nvars <= 2 )
         {
            SCIP_Bool cutoff;

            /* handle all cases with less than three variables in a logicor constraint */
            SCIP_CALL( fixDeleteOrUpgradeCons(scip, cons, conshdlrdata->eventhdlr, conshdlrdata->conshdlrlinear,
                  conshdlrdata->conshdlrsetppc, nfixedvars, nchgbds, nchgcoefs, ndelconss, naddconss, nupgdconss, &cutoff) );

            if( cutoff )
            {
               *result = SCIP_CUTOFF;
               goto TERMINATE;
            }
            else if( *nfixedvars > oldnfixedvars || *nchgbds > oldnchgbds || *nchgcoefs > oldnchgcoefs
               || *ndelconss > oldndelconss  || *nupgdconss > oldnupgdconss )
               *result = SCIP_SUCCESS;

            if( SCIPconsIsDeleted(cons) )
               continue;
         }
      }

      /* remember the first changed constraint to begin the next redundancy round with */
      if( firstchange == INT_MAX && consdata->changed )
         firstchange = c;

      assert(consdata->nvars >= 2 || SCIPconsIsModifiable(cons));
   }

   assert(*result != SCIP_CUTOFF);

   /* fast preprocessing of pairs of logic or constraints, used for equal constraints */
   if( firstchange < nconss && conshdlrdata->presolusehashing )
   {
      /* detect redundant constraints; fast version with hash table instead of pairwise comparison */
      SCIP_CALL( detectRedundantConstraints(scip, SCIPblkmem(scip), conss, nconss, &firstchange, ndelconss) );
   }

   /* preprocess pairs of logic or constraints and apply negated clique presolving */
   if( SCIPisPresolveFinished(scip) )
   {
      SCIP_Bool cutoff = FALSE;

      /* check constraints for redundancy */
      if( conshdlrdata->presolpairwise && (presoltiming & SCIP_PRESOLTIMING_EXHAUSTIVE) != 0 )
      {
         SCIP_CALL( removeRedundantConssAndNonzeros(scip, conss, nconss, &entries, &nentries, conshdlrdata->eventhdlr,
               conshdlrdata->usestrengthening, &firstchange, nfixedvars, ndelconss, nchgcoefs, &cutoff) );

         if( cutoff )
         {
            *result = SCIP_CUTOFF;
            goto TERMINATE;
         }
      }

      if( SCIPisPresolveFinished(scip) )
      {
         /* try to tighten constraints by reducing the number of variables in the constraints using implications and
          * cliques, also derive fixations through them, @see SCIPshrinkDisjunctiveVarSet()
          */
         if( conshdlrdata->useimplications && (presoltiming & SCIP_PRESOLTIMING_EXHAUSTIVE) != 0 )
         {
            SCIP_CALL( shortenConss(scip, conshdlrdata, conshdlrdata->eventhdlr, conss, nconss,
                  &entries, &nentries, nfixedvars, ndelconss, nchgcoefs, &cutoff) );

            if( cutoff )
            {
               *result = SCIP_CUTOFF;
               goto TERMINATE;
            }
         }

         /* check for redundant constraints due to negated clique information */
         if( conshdlrdata->usenegatedclique && (presoltiming & SCIP_PRESOLTIMING_MEDIUM) != 0 )
         {
            SCIP_CALL( removeConstraintsDueToNegCliques(scip, conshdlr, conshdlrdata->conshdlrsetppc,
                  conshdlrdata->eventhdlr, conss, nconss, &entries, &nentries, nfixedvars, ndelconss,
                  nupgdconss, nchgcoefs, &cutoff) );

            if( cutoff )
            {
               *result = SCIP_CUTOFF;
               goto TERMINATE;
            }
         }
      }
   }

 TERMINATE:

   SCIPfreeBufferArray(scip, &entries);

   return SCIP_OKAY;
}


/** propagation conflict resolving method of constraint handler */
static
SCIP_DECL_CONSRESPROP(consRespropLogicor)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;
#ifndef NDEBUG
   SCIP_Bool infervarfound;
#endif
   int v;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(cons != NULL);
   assert(infervar != NULL);
   assert(result != NULL);

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   SCIPdebugMessage("conflict resolving method of logic or constraint handler\n");

   /* the only deductions are variables infered to 1.0 on logic or constraints where all other variables
    * are assigned to zero
    */
   assert(SCIPvarGetLbAtIndex(infervar, bdchgidx, TRUE) > 0.5); /* the inference variable must be assigned to one */

#ifndef NDEBUG
   infervarfound = FALSE;
#endif
   for( v = 0; v < consdata->nvars; ++v )
   {
      if( consdata->vars[v] != infervar )
      {
         /* the reason variable must have been assigned to zero */
         assert(SCIPvarGetUbAtIndex(consdata->vars[v], bdchgidx, FALSE) < 0.5);
         SCIP_CALL( SCIPaddConflictBinvar(scip, consdata->vars[v]) );
      }
#ifndef NDEBUG
      else
      {
         assert(!infervarfound);
         infervarfound = TRUE;
      }
#endif
   }
   assert(infervarfound);

   *result = SCIP_SUCCESS;

   return SCIP_OKAY;
}


/** variable rounding lock method of constraint handler */
static
SCIP_DECL_CONSLOCK(consLockLogicor)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;
   int i;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   /* lock every single coefficient */
   for( i = 0; i < consdata->nvars; ++i )
   {
      SCIP_CALL( SCIPaddVarLocks(scip, consdata->vars[i], nlockspos, nlocksneg) );
   }

   return SCIP_OKAY;
}


/** constraint activation notification method of constraint handler */
static
SCIP_DECL_CONSACTIVE(consActiveLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(cons != NULL);
   assert(SCIPconsIsTransformed(cons));

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);
   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->watchedvar1 == -1 || consdata->watchedvar1 != consdata->watchedvar2);

   SCIPdebugMessage("activating information for logic or constraint <%s>\n", SCIPconsGetName(cons));
   SCIPdebug( SCIP_CALL(consdataPrint(scip, consdata, NULL, TRUE)) );

   /* catch events on watched variables */
   if( consdata->watchedvar1 != -1 )
   {
      SCIP_CALL( SCIPcatchVarEvent(scip, consdata->vars[consdata->watchedvar1],
            SCIP_EVENTTYPE_UBTIGHTENED | SCIP_EVENTTYPE_LBRELAXED, conshdlrdata->eventhdlr, (SCIP_EVENTDATA*)cons,
            &consdata->filterpos1) );
   }
   if( consdata->watchedvar2 != -1 )
   {
      SCIP_CALL( SCIPcatchVarEvent(scip, consdata->vars[consdata->watchedvar2],
            SCIP_EVENTTYPE_UBTIGHTENED | SCIP_EVENTTYPE_LBRELAXED, conshdlrdata->eventhdlr, (SCIP_EVENTDATA*)cons,
            &consdata->filterpos2) );
   }

   return SCIP_OKAY;
}


/** constraint deactivation notification method of constraint handler */
static
SCIP_DECL_CONSDEACTIVE(consDeactiveLogicor)
{  /*lint --e{715}*/
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSDATA* consdata;

   assert(conshdlr != NULL);
   assert(strcmp(SCIPconshdlrGetName(conshdlr), CONSHDLR_NAME) == 0);
   assert(cons != NULL);
   assert(SCIPconsIsTransformed(cons));

   conshdlrdata = SCIPconshdlrGetData(conshdlr);
   assert(conshdlrdata != NULL);
   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);
   assert(consdata->watchedvar1 == -1 || consdata->watchedvar1 != consdata->watchedvar2);

   SCIPdebugMessage("deactivating information for logic or constraint <%s>\n", SCIPconsGetName(cons));
   SCIPdebug( SCIP_CALL(consdataPrint(scip, consdata, NULL, TRUE)) );

   /* drop events on watched variables */
   if( consdata->watchedvar1 != -1 )
   {
      assert(consdata->filterpos1 != -1);
      SCIP_CALL( SCIPdropVarEvent(scip, consdata->vars[consdata->watchedvar1],
            SCIP_EVENTTYPE_UBTIGHTENED | SCIP_EVENTTYPE_LBRELAXED, conshdlrdata->eventhdlr, (SCIP_EVENTDATA*)cons,
            consdata->filterpos1) );
   }
   if( consdata->watchedvar2 != -1 )
   {
      assert(consdata->filterpos2 != -1);
      SCIP_CALL( SCIPdropVarEvent(scip, consdata->vars[consdata->watchedvar2],
            SCIP_EVENTTYPE_UBTIGHTENED | SCIP_EVENTTYPE_LBRELAXED, conshdlrdata->eventhdlr, (SCIP_EVENTDATA*)cons,
            consdata->filterpos2) );
   }

   return SCIP_OKAY;
}


/** constraint display method of constraint handler */
static
SCIP_DECL_CONSPRINT(consPrintLogicor)
{  /*lint --e{715}*/

   assert( scip != NULL );
   assert( conshdlr != NULL );
   assert( cons != NULL );

   SCIP_CALL( consdataPrint(scip, SCIPconsGetData(cons), file, FALSE) );

   return SCIP_OKAY;
}

/** constraint copying method of constraint handler */
static
SCIP_DECL_CONSCOPY(consCopyLogicor)
{  /*lint --e{715}*/
   SCIP_VAR** sourcevars;
   const char* consname;
   int nvars;

   /* get variables and coefficients of the source constraint */
   sourcevars = SCIPgetVarsLogicor(sourcescip, sourcecons);
   nvars = SCIPgetNVarsLogicor(sourcescip, sourcecons);

   if( name != NULL )
      consname = name;
   else
      consname = SCIPconsGetName(sourcecons);

   /* copy the logic using the linear constraint copy method */
   SCIP_CALL( SCIPcopyConsLinear(scip, cons, sourcescip, consname, nvars, sourcevars, NULL,
         1.0, SCIPinfinity(scip), varmap, consmap,
         initial, separate, enforce, check, propagate, local, modifiable, dynamic, removable, stickingatnode, global, valid) );
   assert(cons != NULL);

   return SCIP_OKAY;
}

/** constraint parsing method of constraint handler */
static
SCIP_DECL_CONSPARSE(consParseLogicor)
{  /*lint --e{715}*/
   SCIP_VAR** vars;
   char* strcopy;
   char* endptr;
   char* startptr;
   int requiredsize;
   int varssize;
   int nvars;

   SCIPdebugMessage("parse <%s> as logicor constraint\n", str);

   *success = FALSE;

   /* cutoff "logicor" from the constraint string */
   startptr = strchr(str, '('); /*lint !e158*/

   if( startptr == NULL )
   {
      SCIPerrorMessage("missing starting character '(' parsing logicor\n");
      return SCIP_OKAY;
   }

   /* skip '(' */
   ++startptr;

   /* find end character ')' */
   endptr = strrchr(startptr, ')');

   if( endptr == NULL )
   {
      SCIPerrorMessage("missing ending character ')' parsing logicor\n");
      return SCIP_OKAY;
   }
   assert(endptr >= startptr);

   if( endptr > startptr )
   {
      /* copy string for parsing */
      SCIP_CALL( SCIPduplicateBufferArray(scip, &strcopy, startptr, (int)(endptr-startptr)) );

      varssize = 100;
      nvars = 0;

      /* allocate buffer array for variables */
      SCIP_CALL( SCIPallocBufferArray(scip, &vars, varssize) );

      /* parse string */
      SCIP_CALL( SCIPparseVarsList(scip, strcopy, vars, &nvars, varssize, &requiredsize, &endptr, ',', success) );

      if( *success )
      {
         /* check if the size of the variable array was great enough */
         if( varssize < requiredsize )
         {
            /* reallocate memory */
            varssize = requiredsize;
            SCIP_CALL( SCIPreallocBufferArray(scip, &vars, varssize) );

            /* parse string again with the correct size of the variable array */
            SCIP_CALL( SCIPparseVarsList(scip, strcopy, vars, &nvars, varssize, &requiredsize, &endptr, ',', success) );
         }

         assert(*success);
         assert(varssize >= requiredsize);

         /* create logicor constraint */
         SCIP_CALL( SCIPcreateConsLogicor(scip, cons, name, nvars, vars,
               initial, separate, enforce, check, propagate, local, modifiable, dynamic, removable, stickingatnode) );
      }

      /* free buffers */
      SCIPfreeBufferArray(scip, &vars);
      SCIPfreeBufferArray(scip, &strcopy);
   }
   else
   {
      if( !modifiable )
      {
         SCIPerrorMessage("cannot create empty logicor constraint\n");
         return SCIP_OKAY;
      }

      /* create empty logicor constraint */
      SCIP_CALL( SCIPcreateConsLogicor(scip, cons, name, 0, NULL,
            initial, separate, enforce, check, propagate, local, modifiable, dynamic, removable, stickingatnode) );

      *success = TRUE;
   }

   return SCIP_OKAY;
}

/** constraint method of constraint handler which returns the variables (if possible) */
static
SCIP_DECL_CONSGETVARS(consGetVarsLogicor)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( varssize < consdata->nvars )
      (*success) = FALSE;
   else
   {
      assert(vars != NULL);

      BMScopyMemoryArray(vars, consdata->vars, consdata->nvars);
      (*success) = TRUE;
   }

   return SCIP_OKAY;
}

/** constraint method of constraint handler which returns the number of variables (if possible) */
static
SCIP_DECL_CONSGETNVARS(consGetNVarsLogicor)
{  /*lint --e{715}*/
   SCIP_CONSDATA* consdata;

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   (*nvars) = consdata->nvars;
   (*success) = TRUE;

   return SCIP_OKAY;
}

/*
 * Callback methods of event handler
 */

static
SCIP_DECL_EVENTEXEC(eventExecLogicor)
{  /*lint --e{715}*/
   assert(eventhdlr != NULL);
   assert(eventdata != NULL);
   assert(strcmp(SCIPeventhdlrGetName(eventhdlr), EVENTHDLR_NAME) == 0);
   assert(event != NULL);

   SCIPdebugMessage("exec method of event handler for logic or constraints\n");

   if( SCIPeventGetType(event) == SCIP_EVENTTYPE_LBRELAXED )
   {
      SCIPdebugMessage("enabling constraint cons <%s> at depth %d\n", SCIPconsGetName((SCIP_CONS*)eventdata), SCIPgetDepth(scip));

      SCIP_CALL( SCIPenableCons(scip, (SCIP_CONS*)eventdata) );
      SCIP_CALL( SCIPenableConsPropagation(scip, (SCIP_CONS*)eventdata) );
   }
   else if( SCIPeventGetType(event) == SCIP_EVENTTYPE_UBTIGHTENED )
   {
      SCIP_CALL( SCIPenableConsPropagation(scip, (SCIP_CONS*)eventdata) );
   }

   if( SCIPeventGetType(event) == SCIP_EVENTTYPE_VARFIXED )
   {
      SCIP_VAR* var = SCIPeventGetVar(event);
      SCIP_CONS* cons = (SCIP_CONS*)eventdata;
      SCIP_CONSDATA* consdata;

      assert(cons != NULL);
      consdata = SCIPconsGetData(cons);
      assert(consdata != NULL);

      /* we only catch this event in presolving stage */
      assert(SCIPgetStage(scip) == SCIP_STAGE_PRESOLVING);
      assert(var != NULL);

      consdata->presolved = FALSE;

      if( SCIPvarGetStatus(var) != SCIP_VARSTATUS_FIXED )
      {
         if( SCIPconsIsActive(cons) )
         {
            if( SCIPvarGetLbGlobal(var) < 0.5 && SCIPvarGetUbGlobal(var) > 0.5 )
               consdata->merged = FALSE;

            if( !consdata->existmultaggr )
            {
               if( SCIPvarGetStatus(SCIPvarGetProbvar(var)) == SCIP_VARSTATUS_MULTAGGR )
                  consdata->existmultaggr = TRUE;
            }
         }
      }
   }

   return SCIP_OKAY;
}


/*
 * Callback methods of conflict handler
 */

static
SCIP_DECL_CONFLICTEXEC(conflictExecLogicor)
{  /*lint --e{715}*/
   SCIP_VAR** vars;
   int i;

   assert(conflicthdlr != NULL);
   assert(strcmp(SCIPconflicthdlrGetName(conflicthdlr), CONFLICTHDLR_NAME) == 0);
   assert(bdchginfos != NULL || nbdchginfos == 0);
   assert(result != NULL);

   *result = SCIP_DIDNOTRUN;

   /* don't process already resolved conflicts */
   if( resolved )
      return SCIP_OKAY;

   /* if the conflict consists of only two (binary) variables, it will be handled by the setppc conflict handler */
   if( nbdchginfos == 2 )
      return SCIP_OKAY;

   *result = SCIP_DIDNOTFIND;

   /* create array of variables in conflict constraint */
   SCIP_CALL( SCIPallocBufferArray(scip, &vars, nbdchginfos) );
   for( i = 0; i < nbdchginfos; ++i )
   {
      assert(bdchginfos != NULL); /* for flexelint */
      assert(bdchginfos[i] != NULL);

      vars[i] = SCIPbdchginfoGetVar(bdchginfos[i]);

      /* we can only treat binary variables */
      if( !SCIPvarIsBinary(vars[i]) )
         break;

      /* if the variable is fixed to one in the conflict set, we have to use its negation */
      if( SCIPbdchginfoGetNewbound(bdchginfos[i]) > 0.5 )
      {
         SCIP_CALL( SCIPgetNegatedVar(scip, vars[i], &vars[i]) );
      }
   }

   if( i == nbdchginfos )
   {
      SCIP_CONS* cons;
      char consname[SCIP_MAXSTRLEN];

      /* create a constraint out of the conflict set */
      (void) SCIPsnprintf(consname, SCIP_MAXSTRLEN, "cf%d_%"SCIP_LONGINT_FORMAT, SCIPgetNRuns(scip), SCIPgetNConflictConssApplied(scip));
      SCIP_CALL( SCIPcreateConsLogicor(scip, &cons, consname, nbdchginfos, vars, 
            FALSE, separate, FALSE, FALSE, TRUE, local, FALSE, dynamic, removable, FALSE) );
      SCIP_CALL( SCIPaddConsNode(scip, node, cons, validnode) );
      SCIP_CALL( SCIPreleaseCons(scip, &cons) );

      *result = SCIP_CONSADDED;
   }

   /* free temporary memory */
   SCIPfreeBufferArray(scip, &vars);

   return SCIP_OKAY;
}


/*
 * constraint specific interface methods
 */

/** creates the handler for logic or constraints and includes it in SCIP */
SCIP_RETCODE SCIPincludeConshdlrLogicor(
   SCIP*                 scip                /**< SCIP data structure */
   )
{
   SCIP_CONSHDLRDATA* conshdlrdata;
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONFLICTHDLR* conflicthdlr;
   SCIP_EVENTHDLR* eventhdlr;

   /* create event handler for events on watched variables */
   SCIP_CALL( SCIPincludeEventhdlrBasic(scip, &eventhdlr, EVENTHDLR_NAME, EVENTHDLR_DESC,
         eventExecLogicor, NULL) );

   /* create conflict handler for logic or constraints */
   SCIP_CALL( SCIPincludeConflicthdlrBasic(scip, &conflicthdlr, CONFLICTHDLR_NAME, CONFLICTHDLR_DESC, CONFLICTHDLR_PRIORITY,
         conflictExecLogicor, NULL) );

   /* create constraint handler data */
   SCIP_CALL( conshdlrdataCreate(scip, &conshdlrdata, eventhdlr) );

   /* include constraint handler */
   SCIP_CALL( SCIPincludeConshdlrBasic(scip, &conshdlr, CONSHDLR_NAME, CONSHDLR_DESC,
         CONSHDLR_ENFOPRIORITY, CONSHDLR_CHECKPRIORITY, CONSHDLR_EAGERFREQ, CONSHDLR_NEEDSCONS,
         consEnfolpLogicor, consEnfopsLogicor, consCheckLogicor, consLockLogicor,
         conshdlrdata) );
   assert(conshdlr != NULL);

   /* set non-fundamental callbacks via specific setter functions */
   SCIP_CALL( SCIPsetConshdlrActive(scip, conshdlr, consActiveLogicor) );
   SCIP_CALL( SCIPsetConshdlrCopy(scip, conshdlr, conshdlrCopyLogicor, consCopyLogicor) );
   SCIP_CALL( SCIPsetConshdlrDeactive(scip, conshdlr, consDeactiveLogicor) );
   SCIP_CALL( SCIPsetConshdlrDelete(scip, conshdlr, consDeleteLogicor) );
   SCIP_CALL( SCIPsetConshdlrExitpre(scip, conshdlr, consExitpreLogicor) );
   SCIP_CALL( SCIPsetConshdlrExitsol(scip, conshdlr, consExitsolLogicor) );
   SCIP_CALL( SCIPsetConshdlrFree(scip, conshdlr, consFreeLogicor) );
   SCIP_CALL( SCIPsetConshdlrGetVars(scip, conshdlr, consGetVarsLogicor) );
   SCIP_CALL( SCIPsetConshdlrGetNVars(scip, conshdlr, consGetNVarsLogicor) );
   SCIP_CALL( SCIPsetConshdlrInitpre(scip, conshdlr, consInitpreLogicor) );
   SCIP_CALL( SCIPsetConshdlrInitlp(scip, conshdlr, consInitlpLogicor) );
   SCIP_CALL( SCIPsetConshdlrParse(scip, conshdlr, consParseLogicor) );
   SCIP_CALL( SCIPsetConshdlrPresol(scip, conshdlr, consPresolLogicor,CONSHDLR_MAXPREROUNDS, CONSHDLR_PRESOLTIMING) );
   SCIP_CALL( SCIPsetConshdlrPrint(scip, conshdlr, consPrintLogicor) );
   SCIP_CALL( SCIPsetConshdlrProp(scip, conshdlr, consPropLogicor, CONSHDLR_PROPFREQ, CONSHDLR_DELAYPROP,
         CONSHDLR_PROP_TIMING) );
   SCIP_CALL( SCIPsetConshdlrResprop(scip, conshdlr, consRespropLogicor) );
   SCIP_CALL( SCIPsetConshdlrSepa(scip, conshdlr, consSepalpLogicor, consSepasolLogicor, CONSHDLR_SEPAFREQ,
         CONSHDLR_SEPAPRIORITY, CONSHDLR_DELAYSEPA) );
   SCIP_CALL( SCIPsetConshdlrTrans(scip, conshdlr, consTransLogicor) );

   conshdlrdata->conshdlrlinear = SCIPfindConshdlr(scip, "linear");
   conshdlrdata->conshdlrsetppc = SCIPfindConshdlr(scip, "setppc");

   if( conshdlrdata->conshdlrlinear != NULL )
   {
      /* include the linear constraint to logicor constraint upgrade in the linear constraint handler */
      SCIP_CALL( SCIPincludeLinconsUpgrade(scip, linconsUpgdLogicor, LINCONSUPGD_PRIORITY, CONSHDLR_NAME) );
   }

   /* logic or constraint handler parameters */
   SCIP_CALL( SCIPaddBoolParam(scip,
         "constraints/logicor/presolpairwise",
         "should pairwise constraint comparison be performed in presolving?",
         &conshdlrdata->presolpairwise, TRUE, DEFAULT_PRESOLPAIRWISE, NULL, NULL) );
   SCIP_CALL( SCIPaddBoolParam(scip,
         "constraints/logicor/presolusehashing",
         "should hash table be used for detecting redundant constraints in advance",
         &conshdlrdata->presolusehashing, TRUE, DEFAULT_PRESOLUSEHASHING, NULL, NULL) );
   SCIP_CALL( SCIPaddBoolParam(scip,
         "constraints/logicor/dualpresolving",
         "should dual presolving steps be performed?",
         &conshdlrdata->dualpresolving, TRUE, DEFAULT_DUALPRESOLVING, NULL, NULL) );
   SCIP_CALL( SCIPaddBoolParam(scip,
         "constraints/logicor/negatedclique",
         "should negated clique information be used in presolving",
         &conshdlrdata->usenegatedclique, TRUE, DEFAULT_NEGATEDCLIQUE, NULL, NULL) );
   SCIP_CALL( SCIPaddBoolParam(scip,
         "constraints/logicor/implications",
         "should implications/cliques be used in presolving",
         &conshdlrdata->useimplications, TRUE, DEFAULT_IMPLICATIONS, NULL, NULL) );
   SCIP_CALL( SCIPaddBoolParam(scip,
         "constraints/logicor/strengthen",
         "should pairwise constraint comparison try to strengthen constraints by removing superflous non-zeros?",
         &conshdlrdata->usestrengthening, TRUE, DEFAULT_STRENGTHEN, NULL, NULL) );

   return SCIP_OKAY;
}


/** creates and captures a logic or constraint
 *
 *  @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 */
SCIP_RETCODE SCIPcreateConsLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nvars,              /**< number of variables in the constraint */
   SCIP_VAR**            vars,               /**< array with variables of constraint entries */
   SCIP_Bool             initial,            /**< should the LP relaxation of constraint be in the initial LP?
                                              *   Usually set to TRUE. Set to FALSE for 'lazy constraints'. */
   SCIP_Bool             separate,           /**< should the constraint be separated during LP processing?
                                              *   Usually set to TRUE. */
   SCIP_Bool             enforce,            /**< should the constraint be enforced during node processing?
                                              *   TRUE for model constraints, FALSE for additional, redundant constraints. */
   SCIP_Bool             check,              /**< should the constraint be checked for feasibility?
                                              *   TRUE for model constraints, FALSE for additional, redundant constraints. */
   SCIP_Bool             propagate,          /**< should the constraint be propagated during node processing?
                                              *   Usually set to TRUE. */
   SCIP_Bool             local,              /**< is constraint only valid locally?
                                              *   Usually set to FALSE. Has to be set to TRUE, e.g., for branching constraints. */
   SCIP_Bool             modifiable,         /**< is constraint modifiable (subject to column generation)?
                                              *   Usually set to FALSE. In column generation applications, set to TRUE if pricing
                                              *   adds coefficients to this constraint. */
   SCIP_Bool             dynamic,            /**< is constraint subject to aging?
                                              *   Usually set to FALSE. Set to TRUE for own cuts which 
                                              *   are separated as constraints. */
   SCIP_Bool             removable,          /**< should the relaxation be removed from the LP due to aging or cleanup?
                                              *   Usually set to FALSE. Set to TRUE for 'lazy constraints' and 'user cuts'. */
   SCIP_Bool             stickingatnode      /**< should the constraint always be kept at the node where it was added, even
                                              *   if it may be moved to a more global node?
                                              *   Usually set to FALSE. Set to TRUE to for constraints that represent node data. */
   )
{
   SCIP_CONSHDLR* conshdlr;
   SCIP_CONSDATA* consdata;

   assert(scip != NULL);

   /* find the logicor constraint handler */
   conshdlr = SCIPfindConshdlr(scip, CONSHDLR_NAME);
   if( conshdlr == NULL )
   {
      SCIPerrorMessage("logic or constraint handler not found\n");
      return SCIP_INVALIDCALL;
   }

   /* create the constraint specific data */
   SCIP_CALL( consdataCreate(scip, &consdata, nvars, vars) );

   /* create constraint */
   SCIP_CALL( SCIPcreateCons(scip, cons, name, conshdlr, consdata, initial, separate, enforce, check, propagate,
         local, modifiable, dynamic, removable, stickingatnode) );

   if( SCIPisTransformed(scip) && SCIPgetStage(scip) == SCIP_STAGE_PRESOLVING )
   {
      SCIP_CONSHDLRDATA* conshdlrdata;
      int v;

      conshdlrdata = SCIPconshdlrGetData(conshdlr);
      assert(conshdlrdata != NULL);

      for( v = consdata->nvars - 1; v >= 0; --v )
      {
         SCIP_CALL( SCIPcatchVarEvent(scip, consdata->vars[v], SCIP_EVENTTYPE_VARFIXED, conshdlrdata->eventhdlr,
               (SCIP_EVENTDATA*)(*cons), NULL) );
      }
   }

   return SCIP_OKAY;
}

/** creates and captures a logicor constraint
 *  in its most basic version, i. e., all constraint flags are set to their basic value as explained for the
 *  method SCIPcreateConsLogicor(); all flags can be set via SCIPsetConsFLAGNAME-methods in scip.h
 *
 *  @see SCIPcreateConsLogicor() for information about the basic constraint flag configuration
 *
 *  @note the constraint gets captured, hence at one point you have to release it using the method SCIPreleaseCons()
 */
SCIP_RETCODE SCIPcreateConsBasicLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS**           cons,               /**< pointer to hold the created constraint */
   const char*           name,               /**< name of constraint */
   int                   nvars,              /**< number of variables in the constraint */
   SCIP_VAR**            vars                /**< array with variables of constraint entries */
   )
{
   assert(scip != NULL);

   SCIP_CALL( SCIPcreateConsLogicor(scip, cons, name, nvars, vars,
         TRUE, TRUE, TRUE, TRUE, TRUE, FALSE, FALSE, FALSE, FALSE, FALSE) );

   return SCIP_OKAY;
}

/** adds coefficient in logic or constraint */
SCIP_RETCODE SCIPaddCoefLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons,               /**< logicor constraint */
   SCIP_VAR*             var                 /**< variable to add to the constraint */
   )
{
   assert(var != NULL);

   /*debugMessage("adding variable <%s> to logicor constraint <%s>\n",
     SCIPvarGetName(var), SCIPconsGetName(cons));*/

   if( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not a logic or constraint\n");
      return SCIP_INVALIDDATA;
   }

   SCIP_CALL( addCoef(scip, cons, var) );

   return SCIP_OKAY;
}

/** gets number of variables in logic or constraint */
int SCIPgetNVarsLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint data */
   )
{
   SCIP_CONSDATA* consdata;

   if( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not a logic or constraint\n");
      SCIPABORT();
      return -1;  /*lint !e527*/
   }

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   return consdata->nvars;
}

/** gets array of variables in logic or constraint */
SCIP_VAR** SCIPgetVarsLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint data */
   )
{
   SCIP_CONSDATA* consdata;

   if( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not a logic or constraint\n");
      SCIPABORT();
      return NULL;  /*lint !e527*/
   }

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   return consdata->vars;
}

/** gets the dual solution of the logic or constraint in the current LP */
SCIP_Real SCIPgetDualsolLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint data */
   )
{
   SCIP_CONSDATA* consdata;

   if( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not a logic or constraint\n");
      SCIPABORT();
      return SCIP_INVALID;  /*lint !e527*/
   }

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( consdata->row != NULL )
      return SCIProwGetDualsol(consdata->row);
   else
      return 0.0;
}

/** gets the dual Farkas value of the logic or constraint in the current infeasible LP */
SCIP_Real SCIPgetDualfarkasLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint data */
   )
{
   SCIP_CONSDATA* consdata;

   if( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not a logic or constraint\n");
      SCIPABORT();
      return SCIP_INVALID;  /*lint !e527*/
   }

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   if( consdata->row != NULL )
      return SCIProwGetDualfarkas(consdata->row);
   else
      return 0.0;
}

/** returns the linear relaxation of the given logic or constraint; may return NULL if no LP row was yet created;
 *  the user must not modify the row!
 */
SCIP_ROW* SCIPgetRowLogicor(
   SCIP*                 scip,               /**< SCIP data structure */
   SCIP_CONS*            cons                /**< constraint data */
   )
{
   SCIP_CONSDATA* consdata;

   if( strcmp(SCIPconshdlrGetName(SCIPconsGetHdlr(cons)), CONSHDLR_NAME) != 0 )
   {
      SCIPerrorMessage("constraint is not a logic or constraint\n");
      SCIPABORT();
      return NULL;  /*lint !e527*/
   }

   consdata = SCIPconsGetData(cons);
   assert(consdata != NULL);

   return consdata->row;
}