[2051] | 1 | /* |
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| 2 | * Copyright 1997, Regents of the University of Minnesota |
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| 3 | * |
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| 4 | * mincover.c |
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| 5 | * |
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| 6 | * This file implements the minimum cover algorithm |
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| 7 | * |
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| 8 | * Started 8/1/97 |
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| 9 | * George |
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| 10 | * |
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| 11 | * $Id: mincover.c,v 1.1 1998/11/27 17:59:22 karypis Exp $ |
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| 12 | */ |
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| 13 | |
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| 14 | #include <metis.h> |
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| 15 | |
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| 16 | /************************************************************************* |
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| 17 | * Constants used by mincover algorithm |
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| 18 | **************************************************************************/ |
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| 19 | #define INCOL 10 |
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| 20 | #define INROW 20 |
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| 21 | #define VC 1 |
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| 22 | #define SC 2 |
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| 23 | #define HC 3 |
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| 24 | #define VR 4 |
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| 25 | #define SR 5 |
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| 26 | #define HR 6 |
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| 27 | |
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| 28 | |
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| 29 | /************************************************************************* |
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| 30 | * This function returns the min-cover of a bipartite graph. |
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| 31 | * The algorithm used is due to Hopcroft and Karp as modified by Duff etal |
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| 32 | * adj: the adjacency list of the bipartite graph |
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| 33 | * asize: the number of vertices in the first part of the bipartite graph |
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| 34 | * bsize-asize: the number of vertices in the second part |
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| 35 | * 0..(asize-1) > A vertices |
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| 36 | * asize..bsize > B vertices |
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| 37 | * |
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| 38 | * Returns: |
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| 39 | * cover : the actual cover (array) |
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| 40 | * csize : the size of the cover |
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| 41 | **************************************************************************/ |
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| 42 | void MinCover(idxtype *xadj, idxtype *adjncy, int asize, int bsize, idxtype *cover, int *csize) |
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| 43 | { |
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| 44 | int i, j; |
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| 45 | idxtype *mate, *queue, *flag, *level, *lst; |
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| 46 | int fptr, rptr, lstptr; |
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| 47 | int row, maxlevel, col; |
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| 48 | |
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| 49 | mate = idxsmalloc(bsize, -1, "MinCover: mate"); |
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| 50 | flag = idxmalloc(bsize, "MinCover: flag"); |
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| 51 | level = idxmalloc(bsize, "MinCover: level"); |
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| 52 | queue = idxmalloc(bsize, "MinCover: queue"); |
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| 53 | lst = idxmalloc(bsize, "MinCover: lst"); |
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| 54 | |
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| 55 | /* Get a cheap matching */ |
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| 56 | for (i=0; i<asize; i++) { |
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| 57 | for (j=xadj[i]; j<xadj[i+1]; j++) { |
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| 58 | if (mate[adjncy[j]] == -1) { |
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| 59 | mate[i] = adjncy[j]; |
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| 60 | mate[adjncy[j]] = i; |
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| 61 | break; |
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| 62 | } |
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| 63 | } |
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| 64 | } |
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| 65 | |
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| 66 | /* Get into the main loop */ |
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| 67 | while (1) { |
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| 68 | /* Initialization */ |
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| 69 | fptr = rptr = 0; /* Empty Queue */ |
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| 70 | lstptr = 0; /* Empty List */ |
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| 71 | for (i=0; i<bsize; i++) { |
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| 72 | level[i] = -1; |
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| 73 | flag[i] = 0; |
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| 74 | } |
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| 75 | maxlevel = bsize; |
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| 76 | |
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| 77 | /* Insert free nodes into the queue */ |
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| 78 | for (i=0; i<asize; i++) |
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| 79 | if (mate[i] == -1) { |
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| 80 | queue[rptr++] = i; |
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| 81 | level[i] = 0; |
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| 82 | } |
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| 83 | |
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| 84 | /* Perform the BFS */ |
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| 85 | while (fptr != rptr) { |
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| 86 | row = queue[fptr++]; |
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| 87 | if (level[row] < maxlevel) { |
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| 88 | flag[row] = 1; |
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| 89 | for (j=xadj[row]; j<xadj[row+1]; j++) { |
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| 90 | col = adjncy[j]; |
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| 91 | if (!flag[col]) { /* If this column has not been accessed yet */ |
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| 92 | flag[col] = 1; |
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| 93 | if (mate[col] == -1) { /* Free column node was found */ |
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| 94 | maxlevel = level[row]; |
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| 95 | lst[lstptr++] = col; |
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| 96 | } |
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| 97 | else { /* This column node is matched */ |
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| 98 | if (flag[mate[col]]) |
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| 99 | printf("\nSomething wrong, flag[%d] is 1",mate[col]); |
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| 100 | queue[rptr++] = mate[col]; |
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| 101 | level[mate[col]] = level[row] + 1; |
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| 102 | } |
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| 103 | } |
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| 104 | } |
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| 105 | } |
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| 106 | } |
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| 107 | |
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| 108 | if (lstptr == 0) |
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| 109 | break; /* No free columns can be reached */ |
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| 110 | |
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| 111 | /* Perform restricted DFS from the free column nodes */ |
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| 112 | for (i=0; i<lstptr; i++) |
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| 113 | MinCover_Augment(xadj, adjncy, lst[i], mate, flag, level, maxlevel); |
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| 114 | } |
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| 115 | |
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| 116 | MinCover_Decompose(xadj, adjncy, asize, bsize, mate, cover, csize); |
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| 117 | |
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| 118 | GKfree(&mate, &flag, &level, &queue, &lst, LTERM); |
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| 119 | |
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| 120 | } |
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| 121 | |
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| 122 | |
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| 123 | /************************************************************************* |
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| 124 | * This function perfoms a restricted DFS and augments matchings |
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| 125 | **************************************************************************/ |
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| 126 | int MinCover_Augment(idxtype *xadj, idxtype *adjncy, int col, idxtype *mate, idxtype *flag, idxtype *level, int maxlevel) |
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| 127 | { |
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| 128 | int i; |
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| 129 | int row = -1; |
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| 130 | int status; |
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| 131 | |
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| 132 | flag[col] = 2; |
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| 133 | for (i=xadj[col]; i<xadj[col+1]; i++) { |
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| 134 | row = adjncy[i]; |
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| 135 | |
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| 136 | if (flag[row] == 1) { /* First time through this row node */ |
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| 137 | if (level[row] == maxlevel) { /* (col, row) is an edge of the G^T */ |
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| 138 | flag[row] = 2; /* Mark this node as being visited */ |
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| 139 | if (maxlevel != 0) |
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| 140 | status = MinCover_Augment(xadj, adjncy, mate[row], mate, flag, level, maxlevel-1); |
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| 141 | else |
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| 142 | status = 1; |
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| 143 | |
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| 144 | if (status) { |
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| 145 | mate[col] = row; |
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| 146 | mate[row] = col; |
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| 147 | return 1; |
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| 148 | } |
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| 149 | } |
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| 150 | } |
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| 151 | } |
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| 152 | |
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| 153 | return 0; |
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| 154 | } |
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| 155 | |
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| 156 | |
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| 157 | |
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| 158 | /************************************************************************* |
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| 159 | * This function performs a coarse decomposition and determines the |
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| 160 | * min-cover. |
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| 161 | * REF: Pothen ACMTrans. on Amth Software |
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| 162 | **************************************************************************/ |
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| 163 | void MinCover_Decompose(idxtype *xadj, idxtype *adjncy, int asize, int bsize, idxtype *mate, idxtype *cover, int *csize) |
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| 164 | { |
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| 165 | int i, k; |
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| 166 | idxtype *where; |
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| 167 | int card[10]; |
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| 168 | |
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| 169 | where = idxmalloc(bsize, "MinCover_Decompose: where"); |
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| 170 | for (i=0; i<10; i++) |
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| 171 | card[i] = 0; |
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| 172 | |
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| 173 | for (i=0; i<asize; i++) |
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| 174 | where[i] = SC; |
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| 175 | for (; i<bsize; i++) |
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| 176 | where[i] = SR; |
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| 177 | |
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| 178 | for (i=0; i<asize; i++) |
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| 179 | if (mate[i] == -1) |
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| 180 | MinCover_ColDFS(xadj, adjncy, i, mate, where, INCOL); |
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| 181 | for (; i<bsize; i++) |
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| 182 | if (mate[i] == -1) |
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| 183 | MinCover_RowDFS(xadj, adjncy, i, mate, where, INROW); |
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| 184 | |
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| 185 | for (i=0; i<bsize; i++) |
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| 186 | card[where[i]]++; |
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| 187 | |
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| 188 | k = 0; |
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| 189 | if (abs(card[VC]+card[SC]-card[HR]) < abs(card[VC]-card[SR]-card[HR])) { /* S = VC+SC+HR */ |
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| 190 | /* printf("%d %d ",vc+sc, hr); */ |
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| 191 | for (i=0; i<bsize; i++) |
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| 192 | if (where[i] == VC || where[i] == SC || where[i] == HR) |
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| 193 | cover[k++] = i; |
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| 194 | } |
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| 195 | else { /* S = VC+SR+HR */ |
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| 196 | /* printf("%d %d ",vc, hr+sr); */ |
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| 197 | for (i=0; i<bsize; i++) |
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| 198 | if (where[i] == VC || where[i] == SR || where[i] == HR) |
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| 199 | cover[k++] = i; |
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| 200 | } |
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| 201 | |
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| 202 | *csize = k; |
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| 203 | free(where); |
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| 204 | |
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| 205 | } |
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| 206 | |
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| 207 | |
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| 208 | /************************************************************************* |
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| 209 | * This function perfoms a dfs starting from an unmatched col node |
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| 210 | * forming alternate paths |
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| 211 | **************************************************************************/ |
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| 212 | void MinCover_ColDFS(idxtype *xadj, idxtype *adjncy, int root, idxtype *mate, idxtype *where, int flag) |
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| 213 | { |
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| 214 | int i; |
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| 215 | |
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| 216 | if (flag == INCOL) { |
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| 217 | if (where[root] == HC) |
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| 218 | return; |
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| 219 | where[root] = HC; |
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| 220 | for (i=xadj[root]; i<xadj[root+1]; i++) |
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| 221 | MinCover_ColDFS(xadj, adjncy, adjncy[i], mate, where, INROW); |
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| 222 | } |
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| 223 | else { |
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| 224 | if (where[root] == HR) |
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| 225 | return; |
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| 226 | where[root] = HR; |
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| 227 | if (mate[root] != -1) |
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| 228 | MinCover_ColDFS(xadj, adjncy, mate[root], mate, where, INCOL); |
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| 229 | } |
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| 230 | |
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| 231 | } |
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| 232 | |
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| 233 | /************************************************************************* |
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| 234 | * This function perfoms a dfs starting from an unmatched col node |
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| 235 | * forming alternate paths |
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| 236 | **************************************************************************/ |
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| 237 | void MinCover_RowDFS(idxtype *xadj, idxtype *adjncy, int root, idxtype *mate, idxtype *where, int flag) |
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| 238 | { |
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| 239 | int i; |
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| 240 | |
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| 241 | if (flag == INROW) { |
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| 242 | if (where[root] == VR) |
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| 243 | return; |
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| 244 | where[root] = VR; |
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| 245 | for (i=xadj[root]; i<xadj[root+1]; i++) |
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| 246 | MinCover_RowDFS(xadj, adjncy, adjncy[i], mate, where, INCOL); |
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| 247 | } |
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| 248 | else { |
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| 249 | if (where[root] == VC) |
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| 250 | return; |
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| 251 | where[root] = VC; |
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| 252 | if (mate[root] != -1) |
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| 253 | MinCover_RowDFS(xadj, adjncy, mate[root], mate, where, INROW); |
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| 254 | } |
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| 255 | |
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| 256 | } |
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| 257 | |
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| 258 | |
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| 259 | |
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