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/* asnhall.c (find bipartite matching of maximum cardinality) */
/***********************************************************************
* This code is part of GLPK (GNU Linear Programming Kit).
*
* Copyright (C) 2009-2016 Andrew Makhorin, Department for Applied
* Informatics, Moscow Aviation Institute, Moscow, Russia. All rights
* reserved. E-mail: <mao@gnu.org>.
*
* GLPK is free software: you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* GLPK is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
* License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
***********************************************************************/
#include "env.h"
#include "glpk.h"
#include "mc21a.h"
/***********************************************************************
* NAME
*
* glp_asnprob_hall - find bipartite matching of maximum cardinality
*
* SYNOPSIS
*
* int glp_asnprob_hall(glp_graph *G, int v_set, int a_x);
*
* DESCRIPTION
*
* The routine glp_asnprob_hall finds a matching of maximal cardinality
* in the specified bipartite graph G. It uses a version of the Fortran
* routine MC21A developed by I.S.Duff [1], which implements Hall's
* algorithm [2].
*
* RETURNS
*
* The routine glp_asnprob_hall returns the cardinality of the matching
* found. However, if the specified graph is incorrect (as detected by
* the routine glp_check_asnprob), the routine returns negative value.
*
* REFERENCES
*
* 1. I.S.Duff, Algorithm 575: Permutations for zero-free diagonal, ACM
* Trans. on Math. Softw. 7 (1981), 387-390.
*
* 2. M.Hall, "An Algorithm for distinct representatives," Amer. Math.
* Monthly 63 (1956), 716-717. */
int glp_asnprob_hall(glp_graph *G, int v_set, int a_x)
{ glp_vertex *v;
glp_arc *a;
int card, i, k, loc, n, n1, n2, xij;
int *num, *icn, *ip, *lenr, *iperm, *pr, *arp, *cv, *out;
if (v_set >= 0 && v_set > G->v_size - (int)sizeof(int))
xerror("glp_asnprob_hall: v_set = %d; invalid offset\n",
v_set);
if (a_x >= 0 && a_x > G->a_size - (int)sizeof(int))
xerror("glp_asnprob_hall: a_x = %d; invalid offset\n", a_x);
if (glp_check_asnprob(G, v_set))
return -1;
/* determine the number of vertices in sets R and S and renumber
vertices in S which correspond to columns of the matrix; skip
all isolated vertices */
num = xcalloc(1+G->nv, sizeof(int));
n1 = n2 = 0;
for (i = 1; i <= G->nv; i++)
{ v = G->v[i];
if (v->in == NULL && v->out != NULL)
n1++, num[i] = 0; /* vertex in R */
else if (v->in != NULL && v->out == NULL)
n2++, num[i] = n2; /* vertex in S */
else
{ xassert(v->in == NULL && v->out == NULL);
num[i] = -1; /* isolated vertex */
}
}
/* the matrix must be square, thus, if it has more columns than
rows, extra rows will be just empty, and vice versa */
n = (n1 >= n2 ? n1 : n2);
/* allocate working arrays */
icn = xcalloc(1+G->na, sizeof(int));
ip = xcalloc(1+n, sizeof(int));
lenr = xcalloc(1+n, sizeof(int));
iperm = xcalloc(1+n, sizeof(int));
pr = xcalloc(1+n, sizeof(int));
arp = xcalloc(1+n, sizeof(int));
cv = xcalloc(1+n, sizeof(int));
out = xcalloc(1+n, sizeof(int));
/* build the adjacency matrix of the bipartite graph in row-wise
format (rows are vertices in R, columns are vertices in S) */
k = 0, loc = 1;
for (i = 1; i <= G->nv; i++)
{ if (num[i] != 0) continue;
/* vertex i in R */
ip[++k] = loc;
v = G->v[i];
for (a = v->out; a != NULL; a = a->t_next)
{ xassert(num[a->head->i] != 0);
icn[loc++] = num[a->head->i];
}
lenr[k] = loc - ip[k];
}
xassert(loc-1 == G->na);
/* make all extra rows empty (all extra columns are empty due to
the row-wise format used) */
for (k++; k <= n; k++)
ip[k] = loc, lenr[k] = 0;
/* find a row permutation that maximizes the number of non-zeros
on the main diagonal */
card = mc21a(n, icn, ip, lenr, iperm, pr, arp, cv, out);
#if 1 /* 18/II-2010 */
/* FIXED: if card = n, arp remains clobbered on exit */
for (i = 1; i <= n; i++)
arp[i] = 0;
for (i = 1; i <= card; i++)
{ k = iperm[i];
xassert(1 <= k && k <= n);
xassert(arp[k] == 0);
arp[k] = i;
}
#endif
/* store solution, if necessary */
if (a_x < 0) goto skip;
k = 0;
for (i = 1; i <= G->nv; i++)
{ if (num[i] != 0) continue;
/* vertex i in R */
k++;
v = G->v[i];
for (a = v->out; a != NULL; a = a->t_next)
{ /* arp[k] is the number of matched column or zero */
if (arp[k] == num[a->head->i])
{ xassert(arp[k] != 0);
xij = 1;
}
else
xij = 0;
memcpy((char *)a->data + a_x, &xij, sizeof(int));
}
}
skip: /* free working arrays */
xfree(num);
xfree(icn);
xfree(ip);
xfree(lenr);
xfree(iperm);
xfree(pr);
xfree(arp);
xfree(cv);
xfree(out);
return card;
}
/* eof */
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