예제 #1
0
  ExecStatus
  ReEq<View0,View1>::propagate(Space& home, const ModEventDelta&) {
    if (b.one())
      GECODE_REWRITE(*this,(Eq<View0,View1>::post(home(*this),x0,x1)));
    if (b.zero())
      GECODE_REWRITE(*this,(Distinct<View0,View1>::post(home(*this),x0,x1)));

    if (x0.assigned() && x1.assigned()) {
      // directly test x0==x1
      GlbRanges<View0> x0lb(x0);
      GlbRanges<View1> x1lb(x1);
      for (; x0lb() && x1lb(); ++x0lb, ++x1lb) {
        if (x0lb.min() != x1lb.min() ||
            x0lb.max() != x1lb.max()) {
          GECODE_ME_CHECK(b.zero_none(home));
          return home.ES_SUBSUMED(*this);
        }
      }
      if (!x0lb() && !x1lb()) {
        GECODE_ME_CHECK(b.one_none(home));
        return home.ES_SUBSUMED(*this);
      } else {
        GECODE_ME_CHECK(b.zero_none(home));
        return home.ES_SUBSUMED(*this);
      }
    }

    // check whether cardinalities still allow equality
    if (x0.cardMin() > x1.cardMax() ||
        x1.cardMin() > x0.cardMax()) {
      GECODE_ME_CHECK(b.zero_none(home));
      return home.ES_SUBSUMED(*this);
    }

    // check glb(x0) subset lub(x1)
    GlbRanges<View0> x0lb(x0);
    LubRanges<View1> x1ub(x1);
    Iter::Ranges::Diff<GlbRanges<View0>, LubRanges<View1> > diff1(x0lb, x1ub);
    if ( diff1() ) {
      GECODE_ME_CHECK(b.zero_none(home));
      return home.ES_SUBSUMED(*this);
    }

    // check glb(x1) subset lub(x0)
    GlbRanges<View1> x1lb(x1);
    LubRanges<View0> x0ub(x0);
    Iter::Ranges::Diff<GlbRanges<View1>, LubRanges<View0> > diff2(x1lb, x0ub);
    if ( diff2() ) {
      GECODE_ME_CHECK(b.zero_none(home));
      return home.ES_SUBSUMED(*this);
    }

    return ES_FIX;
  }
예제 #2
0
  ExecStatus
  ReSubset<View0,View1>::propagate(Space& home, const ModEventDelta&) {
    if (b.one())
      GECODE_REWRITE(*this,(Subset<View0,View1>::post(home(*this),x0,x1)));
    if (b.zero())
      GECODE_REWRITE(*this,(NoSubset<View0,View1>::post(home(*this),x0,x1)));

    // check whether cardinalities still allow subset
    if (x0.cardMin() > x1.cardMax()) {
      GECODE_ME_CHECK(b.zero_none(home));
      return home.ES_SUBSUMED(*this);
    }

    // check lub(x0) subset glb(x1)
    {
      LubRanges<View0> x0ub(x0);
      GlbRanges<View1> x1lb(x1);
      Iter::Ranges::Diff<LubRanges<View0>,GlbRanges<View1> > d(x0ub,x1lb);
      if (!d()) {
        GECODE_ME_CHECK(b.one_none(home));
        return home.ES_SUBSUMED(*this);
      }
    }

    // check glb(x0) subset lub(x1)
    {
      GlbRanges<View0> x0lb(x0);
      LubRanges<View1> x1ub(x1);
      Iter::Ranges::Diff<GlbRanges<View0>,LubRanges<View1> > d(x0lb,x1ub);
      if (d()) {
        GECODE_ME_CHECK(b.zero_none(home));
        return home.ES_SUBSUMED(*this);
      } else if (x0.assigned() && x1.assigned()) {
        GECODE_ME_CHECK(b.one_none(home));
        return home.ES_SUBSUMED(*this);
      }
    }

    if (x0.cardMin() > 0) {
      LubRanges<View0> x0ub(x0);
      LubRanges<View1> x1ub(x1);
      Iter::Ranges::Inter<LubRanges<View0>,LubRanges<View1> >
        i(x0ub,x1ub);
      if (!i()) {
        GECODE_ME_CHECK(b.zero_none(home));
        return home.ES_SUBSUMED(*this);
      }
    }

    return ES_FIX;
  }
예제 #3
0
파일: eq.hpp 프로젝트: akiernan/gecode
  ExecStatus
  Eq<View0,View1>::propagate(Space& home, const ModEventDelta& med) {

    ModEvent me0 = View0::me(med);
    ModEvent me1 = View1::me(med);

    Region r(home);

    if (testSetEventLB(me0,me1)) {
      GlbRanges<View0> x0lb(x0);
      GlbRanges<View1> x1lb(x1);
      Iter::Ranges::Union<GlbRanges<View0>,GlbRanges<View1> > lbu(x0lb,x1lb);
      Iter::Ranges::Cache<Iter::Ranges::Union
        <GlbRanges<View0>, GlbRanges<View1> > > lbuc(r,lbu);
      GECODE_ME_CHECK(x0.includeI(home,lbuc));
      lbuc.reset();
      GECODE_ME_CHECK(x1.includeI(home,lbuc));
    }

    if (testSetEventUB(me0,me1)) {
      LubRanges<View0> x0ub(x0);
      LubRanges<View1> x1ub(x1);
      Iter::Ranges::Inter<LubRanges<View0>,LubRanges<View1> > ubi(x0ub,x1ub);
      Iter::Ranges::Cache<Iter::Ranges::Inter
        <LubRanges<View0>,LubRanges<View1> > > ubic(r,ubi);
      GECODE_ME_CHECK(x0.intersectI(home,ubic));
      ubic.reset();
      GECODE_ME_CHECK(x1.intersectI(home,ubic));
    }

    if (testSetEventCard(me0,me1) ) {
      unsigned int max = std::min(x0.cardMax(),x1.cardMax());
      unsigned int min = std::max(x0.cardMin(),x1.cardMin());
      GECODE_ME_CHECK ( x0.cardMax(home,max) );
      GECODE_ME_CHECK ( x1.cardMax(home,max) );
      GECODE_ME_CHECK ( x0.cardMin(home,min) );
      GECODE_ME_CHECK ( x1.cardMin(home,min) );
    }

    if (x0.assigned()) {
      assert (x1.assigned());
      return home.ES_SUBSUMED(*this);
    }
    return shared(x0,x1) ? ES_NOFIX : ES_FIX;
  }
예제 #4
0
  ExecStatus
  Subset<View0,View1>::propagate(Space& home, const ModEventDelta&) {
    bool oneassigned = x0.assigned() || x1.assigned();
    unsigned int x0glbsize;
    do {
      GlbRanges<View0> x0lb(x0);
      GECODE_ME_CHECK ( x1.includeI(home,x0lb) );
      GECODE_ME_CHECK ( x1.cardMin(home,x0.cardMin()) );
      LubRanges<View1> x1ub(x1);
      x0glbsize = x0.glbSize();
      GECODE_ME_CHECK ( x0.intersectI(home,x1ub) );
      GECODE_ME_CHECK ( x0.cardMax(home,x1.cardMax()) );
    } while (x0.glbSize() > x0glbsize);

    if (x0.cardMin() == x1.cardMax())
      GECODE_REWRITE(*this,(Eq<View0,View1>::post(home(*this),x0,x1)));

    if (shared(x0,x1)) {
      return oneassigned ? home.ES_SUBSUMED(*this) : ES_NOFIX;
    }
    return (x0.assigned() || x1.assigned()) ? home.ES_SUBSUMED(*this) : ES_FIX;
  }
예제 #5
0
파일: union.hpp 프로젝트: Gecode/gecode
  ExecStatus
  Union<View0,View1,View2>::propagate(Space& home, const ModEventDelta& med) {
    // This propagator implements the constraint
    // x2 = x0 u x1

    bool x0ass = x0.assigned();
    bool x1ass = x1.assigned();
    bool x2ass = x2.assigned();

    ModEvent me0 = View0::me(med);
    ModEvent me1 = View1::me(med);
    ModEvent me2 = View2::me(med);

    bool x0ubmod = false;
    bool x1ubmod = false;
    bool modified = false;

    do {

      modified = false;
      do {
        // 4) lub(x2) <= lub(x0) u lub(x1)
        {
          LubRanges<View0> x0ub(x0);
          LubRanges<View1> x1ub(x1);
          Iter::Ranges::Union<LubRanges<View0>, LubRanges<View1> > u2(x0ub,x1ub);
          GECODE_ME_CHECK_MODIFIED(modified, x2.intersectI(home,u2) );
        }

        if (modified || Rel::testSetEventUB(me2) )
          {
            modified = false;
            // 5) x0 <= x2
            LubRanges<View2> x2ub1(x2);
            GECODE_ME_CHECK_MODIFIED(modified, x0.intersectI(home,x2ub1) );
            x0ubmod |= modified;

            // 6) x1 <= x2
            bool modified2=false;
            LubRanges<View2> x2ub2(x2);
            GECODE_ME_CHECK_MODIFIED(modified2, x1.intersectI(home,x2ub2) );
            x1ubmod |= modified2;
            modified |= modified2;
          }

      } while (modified);

      modified = false;
      do {
        bool modifiedOld = modified;
        modified = false;

        if (Rel::testSetEventLB(me2) || Rel::testSetEventUB(me0)
             || x0ubmod || modifiedOld)
          {
            // 1) glb(x0) \ lub(x1) <= glb(x2)
            GlbRanges<View2> x2lb(x2);
            LubRanges<View0> x0ub(x0);
            Iter::Ranges::Diff<GlbRanges<View2>, LubRanges<View0> >
              diff(x2lb, x0ub);
            GECODE_ME_CHECK_MODIFIED(modified, x1.includeI(home,diff) );
          }

        if (Rel::testSetEventLB(me2) || Rel::testSetEventUB(me1)
            || x1ubmod || modifiedOld)
          {
            // 2) glb(x0) \ lub(x2) <= glb(x1)
            GlbRanges<View2> x2lb(x2);
            LubRanges<View1> x1ub(x1);
            Iter::Ranges::Diff<GlbRanges<View2>, LubRanges<View1> >
              diff(x2lb, x1ub);
            GECODE_ME_CHECK_MODIFIED(modified, x0.includeI(home,diff) );
          }

         if (Rel::testSetEventLB(me0,me1) || modified)
          {
            //            modified = false;
            // 3) glb(x1) u glb(x2) <= glb(x0)
            GlbRanges<View0> x0lb(x0);
            GlbRanges<View1> x1lb(x1);
            Iter::Ranges::Union<GlbRanges<View0>, GlbRanges<View1> >
              u1(x0lb,x1lb);
            GECODE_ME_CHECK_MODIFIED(modified, x2.includeI(home,u1) );
          }

      } while(modified);

      modified = false;
      {
        // cardinality
        ExecStatus ret = unionCard(home,modified, x0, x1, x2);
        GECODE_ES_CHECK(ret);
      }

      if (x2.cardMax() == 0) {
        GECODE_ME_CHECK( x0.cardMax(home, 0) );
        GECODE_ME_CHECK( x1.cardMax(home, 0) );
        return home.ES_SUBSUMED(*this);
      }

      if (x0.cardMax() == 0)
        GECODE_REWRITE(*this,(Rel::Eq<View1,View2>::post(home(*this),x1,x2)));
      if (x1.cardMax() == 0)
        GECODE_REWRITE(*this,(Rel::Eq<View0,View2>::post(home(*this),x0,x2)));

    } while(modified);

    if (shared(x0,x1,x2)) {
      return (x0ass && x1ass && x2ass) ? home.ES_SUBSUMED(*this) : ES_NOFIX;
    } else {
      if (x0ass && x1ass && x2ass)
        return home.ES_SUBSUMED(*this);
      if (x0ass != x0.assigned() ||
          x1ass != x1.assigned() ||
          x2ass != x2.assigned()) {
        return ES_NOFIX;
      } else {
         return ES_FIX;
      }
    }
  }
예제 #6
0
파일: union.hpp 프로젝트: akiernan/gecode
  ExecStatus
  ElementUnion<SView,RView>::propagate(Space& home, const ModEventDelta&) {
    Region r(home);
    int n = iv.size();

    bool loopVar;
    do {
      loopVar = false;

      // Cache the upper bound iterator, as we have to
      // modify the upper bound while iterating
      LubRanges<RView> x1ub(x1);
      Iter::Ranges::Cache<LubRanges<RView> > x1ubc(r,x1ub);
      Iter::Ranges::ToValues<Iter::Ranges::Cache<LubRanges<RView> > >
        vx1ub(x1ubc);

      GlbRanges<RView> x1lb(x1);
      Iter::Ranges::Cache<GlbRanges<RView> > x1lbc(r,x1lb);
      Iter::Ranges::ToValues<Iter::Ranges::Cache<GlbRanges<RView> > >
        vx1(x1lbc);

      // In the first iteration, compute in before[i] the union
      // of all the upper bounds of the x_i. At the same time,
      // exclude inconsistent x_i from x1 and remove them from
      // the list, cancel their dependencies.

      GLBndSet sofarBefore(home);
      LUBndSet selectedInter(home, IntSet (Limits::min,
                                   Limits::max));
      GLBndSet* before =
        static_cast<GLBndSet*>(r.ralloc(sizeof(GLBndSet)*n));

      int j = 0;
      int i = 0;

      unsigned int maxCard = 0;
      unsigned int minCard = Limits::card;

      while ( vx1ub() ) {

        // Remove vars at indices not in the upper bound
        if (iv[i].idx < vx1ub.val()) {
          iv[i].view.cancel(home,*this, PC_SET_ANY);
          ++i;
          continue;
        }
        assert(iv[i].idx == vx1ub.val());
        iv[j] = iv[i];

        SView candidate = iv[j].view;
        int candidateInd = iv[j].idx;

        // inter = glb(candidate) & complement(lub(x0))
        GlbRanges<SView> candlb(candidate);
        LubRanges<SView> x0ub(x0);
        Iter::Ranges::Diff<GlbRanges<SView>,
          LubRanges<SView> > diff(candlb, x0ub);

        bool selectSingleInconsistent = false;
        if (x1.cardMax() <= 1) {
          GlbRanges<SView> x0lb(x0);
          LubRanges<SView> candub(candidate);
          Iter::Ranges::Diff<GlbRanges<SView>,
                             LubRanges<SView> > diff2(x0lb, candub);
          selectSingleInconsistent = diff2() || candidate.cardMax() < x0.cardMin();
        }

        // exclude inconsistent x_i
        // an x_i is inconsistent if
        //  * at most one x_i can be selected and there are
        //    elements in x_0 that can't be in x_i
        //    (selectSingleInconsistent)
        //  * its min cardinality is greater than maxCard of x0
        //  * inter is not empty (there are elements in x_i
        //    that can't be in x_0)
        if (selectSingleInconsistent ||
            candidate.cardMin() > x0.cardMax() ||
            diff()) {
          ModEvent me = (x1.exclude(home,candidateInd));
          loopVar |= me_modified(me);
          GECODE_ME_CHECK(me);

          iv[j].view.cancel(home,*this, PC_SET_ANY);
          ++i;
          ++vx1ub;
          continue;
        } else {
          // if x_i is consistent, check whether we know
          // that its index is in x1
          if (vx1() && vx1.val()==candidateInd) {
            // x0 >= candidate, candidate <= x0
            GlbRanges<SView> candlb(candidate);
            ModEvent me = x0.includeI(home,candlb);
            loopVar |= me_modified(me);
            GECODE_ME_CHECK(me);

            LubRanges<SView> x0ub(x0);
            me = candidate.intersectI(home,x0ub);
            loopVar |= me_modified(me);
            GECODE_ME_CHECK(me);
            ++vx1;
          }
          new (&before[j]) GLBndSet(home);
          before[j].update(home,sofarBefore);
          LubRanges<SView> cub(candidate);
          sofarBefore.includeI(home,cub);
          GlbRanges<SView> clb(candidate);
          selectedInter.intersectI(home,clb);
          maxCard = std::max(maxCard, candidate.cardMax());
          minCard = std::min(minCard, candidate.cardMin());
        }

        ++vx1ub;
        ++i; ++j;
      }

      // cancel the variables with index greater than
      // max of lub(x1)
      for (int k=i; k<n; k++) {
        iv[k].view.cancel(home,*this, PC_SET_ANY);
      }
      n = j;
      iv.size(n);

      if (x1.cardMax()==0) {
        // Selector is empty, hence the result must be empty
        {
          GECODE_ME_CHECK(x0.cardMax(home,0));
        }
        for (int i=n; i--;)
          before[i].dispose(home);
        return home.ES_SUBSUMED(*this);
      }

      if (x1.cardMin() > 0) {
        // Selector is not empty, hence the intersection of the
        // possibly selected lower bounds is contained in x0
        BndSetRanges si(selectedInter);
        ModEvent me = x0.includeI(home, si);
        loopVar |= me_modified(me);
        GECODE_ME_CHECK(me);
        me = x0.cardMin(home, minCard);
        loopVar |= me_modified(me);
        GECODE_ME_CHECK(me);
      }
      selectedInter.dispose(home);

      if (x1.cardMax() <= 1) {
        ModEvent me = x0.cardMax(home, maxCard);
        loopVar |= me_modified(me);
        GECODE_ME_CHECK(me);
      }

      {
        // x0 <= sofarBefore
        BndSetRanges sfB(sofarBefore);
        ModEvent me = x0.intersectI(home,sfB);
        loopVar |= me_modified(me);
        GECODE_ME_CHECK(me);
      }

      sofarBefore.dispose(home);

      GLBndSet sofarAfter(home);

      // In the second iteration, this time backwards, compute
      // sofarAfter as the union of all lub(x_j) with j>i
      for (int i=n; i--;) {
        // TODO: check for size of universe here?
        // if (sofarAfter.size() == 0) break;

        // extra = inter(before[i], sofarAfter) - lub(x0)
        BndSetRanges b(before[i]);
        BndSetRanges s(sofarAfter);
        GlbRanges<SView> x0lb(x0);
        Iter::Ranges::Union<BndSetRanges, BndSetRanges> inter(b,s);
        Iter::Ranges::Diff<GlbRanges<SView>,
          Iter::Ranges::Union<BndSetRanges,BndSetRanges> > diff(x0lb, inter);
        if (diff()) {
          ModEvent me = (x1.include(home,iv[i].idx));
          loopVar |= me_modified(me);
          GECODE_ME_CHECK(me);

          // candidate != extra
          me = iv[i].view.includeI(home,diff);
          loopVar |= me_modified(me);
          GECODE_ME_CHECK(me);
        }

        LubRanges<SView> iviub(iv[i].view);
        sofarAfter.includeI(home,iviub);
        before[i].dispose(home);
      }
      sofarAfter.dispose(home);

    } while (loopVar);

    // Test whether we determined x1 without determining x0
    if (x1.assigned() && !x0.assigned()) {
      int ubsize = static_cast<int>(x1.lubSize());
      if (ubsize > 2) {
        assert(ubsize==n);
        ViewArray<SView> is(home,ubsize);
        for (int i=n; i--;)
          is[i]=iv[i].view;
        GECODE_REWRITE(*this,(RelOp::UnionN<SView, SView>
                        ::post(home(*this),is,x0)));
      } else if (ubsize == 2) {
        assert(n==2);
        SView a = iv[0].view;
        SView b = iv[1].view;
        GECODE_REWRITE(*this,(RelOp::Union<SView, SView, SView>
                       ::post(home(*this),a,b,x0)));
      } else if (ubsize == 1) {
        assert(n==1);
        GECODE_REWRITE(*this,(Rel::Eq<SView,SView>::post(home(*this),x0,iv[0].view)));
      } else {
        GECODE_ME_CHECK(x0.cardMax(home, 0));
        return home.ES_SUBSUMED(*this);
      }
    }

    bool allAssigned = true;
    for (int i=iv.size(); i--;) {
      if (!iv[i].view.assigned()) {
        allAssigned = false;
        break;
      }
    }
    if (x0.assigned() && x1.assigned() && allAssigned) {
      return home.ES_SUBSUMED(*this);
    }

    return ES_FIX;
  }
예제 #7
0
  ExecStatus
  ElementUnionConst<SView,RView>::propagate(Space& home, const ModEventDelta&) {
    Region r(home);

    bool* stillSelected = r.alloc<bool>(n_iv);

    bool loopVar;
    do {
      loopVar = false;
      for (int i=n_iv; i--;)
        stillSelected[i] = false;

      // Cache the upper bound iterator, as we have to
      // modify the upper bound while iterating
      LubRanges<RView> x1ub(x1);
      Iter::Ranges::Cache x1ubc(r,x1ub);
      Iter::Ranges::ToValues<Iter::Ranges::Cache>
        vx1ub(x1ubc);

      GlbRanges<RView> x1lb(x1);
      Iter::Ranges::Cache x1lbc(r,x1lb);
      Iter::Ranges::ToValues<Iter::Ranges::Cache>
        vx1(x1lbc);

      // In the first iteration, compute in before[i] the union
      // of all the upper bounds of the x_i. At the same time,
      // exclude inconsistent x_i from x1.

      GLBndSet sofarBefore(home);
      LUBndSet selectedInter(home, IntSet (Limits::min,
                                   Limits::max));
      GLBndSet* before =
        static_cast<GLBndSet*>(r.ralloc(sizeof(GLBndSet)*n_iv));

      unsigned int maxCard = 0;
      unsigned int minCard = Limits::card;

      while (vx1ub()) {
        int i = vx1ub.val();

        IntSetRanges candCardR(iv[i]);
        unsigned int candidateCard = Iter::Ranges::size(candCardR);

        IntSetRanges candlb(iv[i]);
        LubRanges<SView> x0ub(x0);
        Iter::Ranges::Diff<IntSetRanges,
          LubRanges<SView> > diff(candlb, x0ub);

        bool selectSingleInconsistent = false;
        if (x1.cardMax() <= 1) {
          GlbRanges<SView> x0lb(x0);
          IntSetRanges candub(iv[i]);
          Iter::Ranges::Diff<GlbRanges<SView>,
                             IntSetRanges > diff2(x0lb, candub);
          selectSingleInconsistent = diff2() || candidateCard < x0.cardMin();
        }

        // exclude inconsistent x_i
        // an x_i is inconsistent if
        //  * at most one x_i can be selected and there are
        //    elements in x_0 that can't be in x_i
        //    (selectSingleInconsistent)
        //  * its min cardinality is greater than maxCard of x0
        //  * inter is not empty (there are elements in x_i
        //    that can't be in x_0)
        if (selectSingleInconsistent ||
            candidateCard > x0.cardMax() ||
            diff()) {
          ModEvent me = (x1.exclude(home,i));
          loopVar |= me_modified(me);
          GECODE_ME_CHECK(me);
        } else {
          stillSelected[i] = true;
          // if x_i is consistent, check whether we know
          // that its index is in x1
          if (vx1() && vx1.val()==i) {
            // x0 >= candidate, candidate <= x0
            // GlbRanges<SView> candlb(candidate);
            IntSetRanges candlb(iv[i]);
            ModEvent me = x0.includeI(home,candlb);
            loopVar |= me_modified(me);
            GECODE_ME_CHECK(me);
            ++vx1;
          }
          new (&before[i]) GLBndSet(home);
          before[i].update(home,sofarBefore);
          IntSetRanges cub(iv[i]);
          sofarBefore.includeI(home,cub);
          IntSetRanges clb(iv[i]);
          selectedInter.intersectI(home,clb);
          maxCard = std::max(maxCard, candidateCard);
          minCard = std::min(minCard, candidateCard);
        }

        ++vx1ub;
      }

      if (x1.cardMax()==0) {
        // Selector is empty, hence the result must be empty
        {
          GECODE_ME_CHECK(x0.cardMax(home,0));
        }
        for (int i=n_iv; i--;)
          if (stillSelected[i])
            before[i].dispose(home);
        selectedInter.dispose(home);
        sofarBefore.dispose(home);
        return home.ES_SUBSUMED(*this);
      }

      if (x1.cardMin() > 0) {
        // Selector is not empty, hence the intersection of the
        // possibly selected lower bounds is contained in x0
        BndSetRanges si(selectedInter);
        ModEvent me = x0.includeI(home, si);
        loopVar |= me_modified(me);
        GECODE_ME_CHECK(me);
        me = x0.cardMin(home, minCard);
        loopVar |= me_modified(me);
        GECODE_ME_CHECK(me);
      }
      selectedInter.dispose(home);

      if (x1.cardMax() <= 1) {
        ModEvent me = x0.cardMax(home, maxCard);
        loopVar |= me_modified(me);
        GECODE_ME_CHECK(me);
      }

      {
        // x0 <= sofarBefore
        BndSetRanges sfB(sofarBefore);
        ModEvent me = x0.intersectI(home,sfB);
        loopVar |= me_modified(me);
        GECODE_ME_CHECK(me);
      }

      sofarBefore.dispose(home);

      GLBndSet sofarAfter(home);

      // In the second iteration, this time backwards, compute
      // sofarAfter as the union of all lub(x_j) with j>i
      for (int i=n_iv; i--;) {
        if (!stillSelected[i])
          continue;
        BndSetRanges b(before[i]);
        BndSetRanges s(sofarAfter);
        GlbRanges<SView> x0lb(x0);
        Iter::Ranges::Union<BndSetRanges, BndSetRanges> inter(b,s);
        Iter::Ranges::Diff<GlbRanges<SView>,
          Iter::Ranges::Union<BndSetRanges,BndSetRanges> > diff(x0lb, inter);
        if (diff()) {
          ModEvent me = (x1.include(home,i));
          loopVar |= me_modified(me);
          GECODE_ME_CHECK(me);

          // candidate != extra
          IntSetRanges ivi(iv[i]);
          if (!Iter::Ranges::subset(diff, ivi))
            GECODE_ME_CHECK(ME_SET_FAILED);
        }

        IntSetRanges iviub(iv[i]);
        sofarAfter.includeI(home,iviub);
        before[i].dispose(home);
      }
      sofarAfter.dispose(home);

    } while (loopVar);

    if (x1.assigned()) {
      assert(x0.assigned());
      return home.ES_SUBSUMED(*this);
    }

    return ES_FIX;
  }