260 lines
7.2 KiB
C
260 lines
7.2 KiB
C
/*
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* Copyright 1997, Regents of the University of Minnesota
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*
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* mincover.c
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*
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* This file implements the minimum cover algorithm
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*
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* Started 8/1/97
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* George
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*
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* $Id: mincover.c,v 1.2 2002/08/10 06:29:33 karypis Exp $
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*/
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#include <metislib.h>
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/*************************************************************************
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* Constants used by mincover algorithm
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**************************************************************************/
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#define INCOL 10
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#define INROW 20
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#define VC 1
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#define SC 2
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#define HC 3
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#define VR 4
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#define SR 5
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#define HR 6
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/*************************************************************************
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* This function returns the min-cover of a bipartite graph.
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* The algorithm used is due to Hopcroft and Karp as modified by Duff etal
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* adj: the adjacency list of the bipartite graph
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* asize: the number of vertices in the first part of the bipartite graph
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* bsize-asize: the number of vertices in the second part
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* 0..(asize-1) > A vertices
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* asize..bsize > B vertices
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*
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* Returns:
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* cover : the actual cover (array)
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* csize : the size of the cover
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**************************************************************************/
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void MinCover(idxtype *xadj, idxtype *adjncy, idxtype asize, idxtype bsize, idxtype *cover, idxtype *csize)
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{
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idxtype i, j;
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idxtype *mate, *queue, *flag, *level, *lst;
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idxtype fptr, rptr, lstptr;
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idxtype row, maxlevel, col;
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mate = idxsmalloc(bsize, -1, "MinCover: mate");
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flag = idxmalloc(bsize, "MinCover: flag");
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level = idxmalloc(bsize, "MinCover: level");
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queue = idxmalloc(bsize, "MinCover: queue");
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lst = idxmalloc(bsize, "MinCover: lst");
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/* Get a cheap matching */
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for (i=0; i<asize; i++) {
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for (j=xadj[i]; j<xadj[i+1]; j++) {
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if (mate[adjncy[j]] == -1) {
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mate[i] = adjncy[j];
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mate[adjncy[j]] = i;
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break;
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}
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}
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}
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/* Get into the main loop */
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while (1) {
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/* Initialization */
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fptr = rptr = 0; /* Empty Queue */
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lstptr = 0; /* Empty List */
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for (i=0; i<bsize; i++) {
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level[i] = -1;
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flag[i] = 0;
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}
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maxlevel = bsize;
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/* Insert free nodes into the queue */
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for (i=0; i<asize; i++)
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if (mate[i] == -1) {
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queue[rptr++] = i;
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level[i] = 0;
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}
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/* Perform the BFS */
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while (fptr != rptr) {
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row = queue[fptr++];
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if (level[row] < maxlevel) {
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flag[row] = 1;
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for (j=xadj[row]; j<xadj[row+1]; j++) {
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col = adjncy[j];
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if (!flag[col]) { /* If this column has not been accessed yet */
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flag[col] = 1;
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if (mate[col] == -1) { /* Free column node was found */
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maxlevel = level[row];
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lst[lstptr++] = col;
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}
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else { /* This column node is matched */
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if (flag[mate[col]])
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mprintf("\nSomething wrong, flag[%D] is 1",mate[col]);
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queue[rptr++] = mate[col];
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level[mate[col]] = level[row] + 1;
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}
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}
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}
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}
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}
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if (lstptr == 0)
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break; /* No free columns can be reached */
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/* Perform restricted DFS from the free column nodes */
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for (i=0; i<lstptr; i++)
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MinCover_Augment(xadj, adjncy, lst[i], mate, flag, level, maxlevel);
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}
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MinCover_Decompose(xadj, adjncy, asize, bsize, mate, cover, csize);
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gk_free((void **)&mate, &flag, &level, &queue, &lst, LTERM);
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}
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/*************************************************************************
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* This function perfoms a restricted DFS and augments matchings
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**************************************************************************/
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idxtype MinCover_Augment(idxtype *xadj, idxtype *adjncy, idxtype col, idxtype *mate, idxtype *flag, idxtype *level, idxtype maxlevel)
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{
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idxtype i;
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idxtype row = -1;
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idxtype status;
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flag[col] = 2;
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for (i=xadj[col]; i<xadj[col+1]; i++) {
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row = adjncy[i];
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if (flag[row] == 1) { /* First time through this row node */
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if (level[row] == maxlevel) { /* (col, row) is an edge of the G^T */
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flag[row] = 2; /* Mark this node as being visited */
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if (maxlevel != 0)
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status = MinCover_Augment(xadj, adjncy, mate[row], mate, flag, level, maxlevel-1);
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else
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status = 1;
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if (status) {
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mate[col] = row;
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mate[row] = col;
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return 1;
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}
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}
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}
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}
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return 0;
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}
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/*************************************************************************
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* This function performs a coarse decomposition and determines the
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* min-cover.
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* REF: Pothen ACMTrans. on Amth Software
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**************************************************************************/
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void MinCover_Decompose(idxtype *xadj, idxtype *adjncy, idxtype asize, idxtype bsize, idxtype *mate, idxtype *cover, idxtype *csize)
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{
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idxtype i, k;
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idxtype *where;
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idxtype card[10];
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where = idxmalloc(bsize, "MinCover_Decompose: where");
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for (i=0; i<10; i++)
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card[i] = 0;
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for (i=0; i<asize; i++)
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where[i] = SC;
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for (; i<bsize; i++)
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where[i] = SR;
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for (i=0; i<asize; i++)
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if (mate[i] == -1)
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MinCover_ColDFS(xadj, adjncy, i, mate, where, INCOL);
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for (; i<bsize; i++)
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if (mate[i] == -1)
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MinCover_RowDFS(xadj, adjncy, i, mate, where, INROW);
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for (i=0; i<bsize; i++)
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card[where[i]]++;
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k = 0;
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if (idxtype_abs(card[VC]+card[SC]-card[HR]) < idxtype_abs(card[VC]-card[SR]-card[HR])) { /* S = VC+SC+HR */
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/* mprintf("%D %D ",vc+sc, hr); */
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for (i=0; i<bsize; i++)
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if (where[i] == VC || where[i] == SC || where[i] == HR)
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cover[k++] = i;
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}
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else { /* S = VC+SR+HR */
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/* mprintf("%D %D ",vc, hr+sr); */
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for (i=0; i<bsize; i++)
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if (where[i] == VC || where[i] == SR || where[i] == HR)
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cover[k++] = i;
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}
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*csize = k;
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gk_free((void **)&where, LTERM);
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}
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/*************************************************************************
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* This function perfoms a dfs starting from an unmatched col node
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* forming alternate paths
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**************************************************************************/
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void MinCover_ColDFS(idxtype *xadj, idxtype *adjncy, idxtype root, idxtype *mate, idxtype *where, idxtype flag)
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{
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idxtype i;
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if (flag == INCOL) {
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if (where[root] == HC)
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return;
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where[root] = HC;
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for (i=xadj[root]; i<xadj[root+1]; i++)
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MinCover_ColDFS(xadj, adjncy, adjncy[i], mate, where, INROW);
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}
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else {
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if (where[root] == HR)
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return;
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where[root] = HR;
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if (mate[root] != -1)
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MinCover_ColDFS(xadj, adjncy, mate[root], mate, where, INCOL);
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}
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}
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/*************************************************************************
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* This function perfoms a dfs starting from an unmatched col node
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* forming alternate paths
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**************************************************************************/
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void MinCover_RowDFS(idxtype *xadj, idxtype *adjncy, idxtype root, idxtype *mate, idxtype *where, idxtype flag)
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{
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idxtype i;
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if (flag == INROW) {
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if (where[root] == VR)
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return;
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where[root] = VR;
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for (i=xadj[root]; i<xadj[root+1]; i++)
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MinCover_RowDFS(xadj, adjncy, adjncy[i], mate, where, INCOL);
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}
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else {
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if (where[root] == VC)
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return;
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where[root] = VC;
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if (mate[root] != -1)
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MinCover_RowDFS(xadj, adjncy, mate[root], mate, where, INROW);
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}
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}
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