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/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
* Main authors:
* Patrick Pekczynski <pekczynski@ps.uni-sb.de>
*
* Copyright:
* Patrick Pekczynski, 2004
*
* This file is part of Gecode, the generic constraint
* development environment:
* http://www.gecode.org
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
namespace Gecode { namespace Int { namespace Sorted {
/**
* \brief Glover's maximum matching in a bipartite graph
*
* Compute a matching in the bipartite convex intersection graph with
* one partition containing the x views and the other containing
* the y views. The algorithm works with an implicit array structure
* of the intersection graph.
*
* Union-Find Implementation of F.Glover's matching algorithm.
*
* The idea is to mimic a priority queue storing x-indices
* \f$[i_0,\dots, i_{n-1}]\f$, s.t. the upper domain bounds are sorted
* \f$D_{i_0} \leq\dots\leq D_{i_{n-1}}\f$ where \f$ D_{i_0}\f$
* is the top element
*
*/
template<class View>
inline bool
glover(ViewArray<View>& x, ViewArray<View>& y,
int tau[], int phi[], OfflineMinItem sequence[], int vertices[]) {
int xs = x.size();
OfflineMin seq(sequence, vertices, xs);
int s = 0;
seq.makeset();
for (int z = 0; z < xs; z++) { // forall y nodes
int maxy = y[z].max();
// creating the sequence of inserts and extractions from the queue
for( ; s <xs && x[s].min() <= maxy; s++) {
seq[s].iset = z;
seq[z].rank++;
}
}
// offline-min-procedure
for (int i = 0; i < xs; i++) {
// the upper bound of the x-node should be minimal
int perm = tau[i];
// find the iteration where \tau(i) became a matching candidate
int iter = seq[perm].iset;
if (iter<0)
return false;
int j = 0;
j = seq.find_pc(iter);
// check whether the sequence is valid
if (j >= xs)
return false;
// if there is no intersection between the matching candidate
// and the y node then there exists NO perfect matching
if (x[perm].max() < y[j].min())
return false;
phi[j] = perm;
seq[perm].iset = -5; //remove from candidate set
int sqjsucc = seq[j].succ;
if (sqjsucc < xs) {
seq.unite(j,sqjsucc,sqjsucc);
} else {
seq[seq[j].root].name = sqjsucc; // end of sequence achieved
}
// adjust tree list
int pr = seq[j].pred;
if (pr != -1)
seq[pr].succ = sqjsucc;
if (sqjsucc != xs)
seq[sqjsucc].pred = pr;
}
return true;
}
/**
* \brief Symmetric glover function for the upper domain bounds
*
*/
template<class View>
inline bool
revglover(ViewArray<View>& x, ViewArray<View>& y,
int tau[], int phiprime[], OfflineMinItem sequence[],
int vertices[]) {
int xs = x.size();
OfflineMin seq(sequence, vertices, xs);
int s = xs - 1;
seq.makeset();
int miny = 0;
for (int z = xs; z--; ) { // forall y nodes
miny = y[z].min();
// creating the sequence of inserts and extractions from the queue
for ( ; s > -1 && x[tau[s]].max() >= miny; s--) {
seq[tau[s]].iset = z;
seq[z].rank++;
}
}
// offline-min-procedure
for (int i = xs; i--; ) {
int perm = i;
int iter = seq[perm].iset;
if (iter < 0)
return false;
int j = 0;
j = seq.find_pc(iter);
if (j <= -1)
return false;
// if there is no intersection between the matching candidate
// and the y node then there exists NO perfect matching
if (x[perm].min() > y[j].max())
return false;
phiprime[j] = perm;
seq[perm].iset = -5;
int sqjsucc = seq[j].pred;
if (sqjsucc >= 0) {
seq.unite(j, sqjsucc, sqjsucc);
} else {
seq[seq[j].root].name = sqjsucc; // end of sequence achieved
}
// adjust tree list
int pr = seq[j].succ;
if (pr != xs)
seq[pr].pred = sqjsucc;
if (sqjsucc != -1)
seq[sqjsucc].succ = pr;
}
return true;
}
}}}
// STATISTICS: int-prop
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