[1] | 1 | /* glpnet09.c */ |
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| 2 | |
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| 3 | /*********************************************************************** |
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| 4 | * This code is part of GLPK (GNU Linear Programming Kit). |
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| 5 | * |
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| 6 | * Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, |
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| 7 | * 2009, 2010 Andrew Makhorin, Department for Applied Informatics, |
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| 8 | * Moscow Aviation Institute, Moscow, Russia. All rights reserved. |
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| 9 | * E-mail: <mao@gnu.org>. |
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| 10 | * |
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| 11 | * GLPK is free software: you can redistribute it and/or modify it |
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| 12 | * under the terms of the GNU General Public License as published by |
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| 13 | * the Free Software Foundation, either version 3 of the License, or |
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| 14 | * (at your option) any later version. |
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| 15 | * |
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| 16 | * GLPK is distributed in the hope that it will be useful, but WITHOUT |
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| 17 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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| 18 | * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public |
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| 19 | * License for more details. |
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| 20 | * |
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| 21 | * You should have received a copy of the GNU General Public License |
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| 22 | * along with GLPK. If not, see <http://www.gnu.org/licenses/>. |
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| 23 | ***********************************************************************/ |
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| 24 | |
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| 25 | #include "glpapi.h" |
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| 26 | #include "glpnet.h" |
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| 27 | |
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| 28 | /*********************************************************************** |
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| 29 | * NAME |
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| 30 | * |
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| 31 | * kellerman - cover edges by cliques with Kellerman's heuristic |
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| 32 | * |
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| 33 | * SYNOPSIS |
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| 34 | * |
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| 35 | * #include "glpnet.h" |
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| 36 | * int kellerman(int n, int (*func)(void *info, int i, int ind[]), |
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| 37 | * void *info, glp_graph *H); |
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| 38 | * |
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| 39 | * DESCRIPTION |
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| 40 | * |
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| 41 | * The routine kellerman implements Kellerman's heuristic algorithm |
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| 42 | * to find a minimal set of cliques which cover all edges of specified |
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| 43 | * graph G = (V, E). |
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| 44 | * |
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| 45 | * The parameter n specifies the number of vertices |V|, n >= 0. |
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| 46 | * |
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| 47 | * Formal routine func specifies the set of edges E in the following |
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| 48 | * way. Running the routine kellerman calls the routine func and passes |
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| 49 | * to it parameter i, which is the number of some vertex, 1 <= i <= n. |
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| 50 | * In response the routine func should store numbers of all vertices |
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| 51 | * adjacent to vertex i to locations ind[1], ind[2], ..., ind[len] and |
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| 52 | * return the value of len, which is the number of adjacent vertices, |
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| 53 | * 0 <= len <= n. Self-loops are allowed, but ignored. Multiple edges |
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| 54 | * are not allowed. |
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| 55 | * |
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| 56 | * The parameter info is a transit pointer (magic cookie) passed to the |
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| 57 | * formal routine func as its first parameter. |
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| 58 | * |
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| 59 | * The result provided by the routine kellerman is the bipartite graph |
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| 60 | * H = (V union C, F), which defines the covering found. (The program |
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| 61 | * object of type glp_graph specified by the parameter H should be |
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| 62 | * previously created with the routine glp_create_graph. On entry the |
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| 63 | * routine kellerman erases the content of this object with the routine |
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| 64 | * glp_erase_graph.) Vertices of first part V correspond to vertices of |
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| 65 | * the graph G and have the same ordinal numbers 1, 2, ..., n. Vertices |
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| 66 | * of second part C correspond to cliques and have ordinal numbers |
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| 67 | * n+1, n+2, ..., n+k, where k is the total number of cliques in the |
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| 68 | * edge covering found. Every edge f in F in the program object H is |
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| 69 | * represented as arc f = (i->j), where i in V and j in C, which means |
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| 70 | * that vertex i of the graph G is in clique C[j], 1 <= j <= k. (Thus, |
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| 71 | * if two vertices of the graph G are in the same clique, these vertices |
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| 72 | * are adjacent in G, and corresponding edge is covered by that clique.) |
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| 73 | * |
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| 74 | * RETURNS |
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| 75 | * |
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| 76 | * The routine Kellerman returns k, the total number of cliques in the |
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| 77 | * edge covering found. |
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| 78 | * |
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| 79 | * REFERENCE |
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| 80 | * |
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| 81 | * For more details see: glpk/doc/notes/keller.pdf (in Russian). */ |
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| 82 | |
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| 83 | struct set |
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| 84 | { /* set of vertices */ |
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| 85 | int size; |
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| 86 | /* size (cardinality) of the set, 0 <= card <= n */ |
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| 87 | int *list; /* int list[1+n]; */ |
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| 88 | /* the set contains vertices list[1,...,size] */ |
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| 89 | int *pos; /* int pos[1+n]; */ |
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| 90 | /* pos[i] > 0 means that vertex i is in the set and |
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| 91 | list[pos[i]] = i; pos[i] = 0 means that vertex i is not in |
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| 92 | the set */ |
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| 93 | }; |
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| 94 | |
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| 95 | int kellerman(int n, int (*func)(void *info, int i, int ind[]), |
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| 96 | void *info, void /* glp_graph */ *H_) |
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| 97 | { glp_graph *H = H_; |
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| 98 | struct set W_, *W = &W_, V_, *V = &V_; |
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| 99 | glp_arc *a; |
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| 100 | int i, j, k, m, t, len, card, best; |
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| 101 | xassert(n >= 0); |
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| 102 | /* H := (V, 0; 0), where V is the set of vertices of graph G */ |
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| 103 | glp_erase_graph(H, H->v_size, H->a_size); |
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| 104 | glp_add_vertices(H, n); |
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| 105 | /* W := 0 */ |
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| 106 | W->size = 0; |
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| 107 | W->list = xcalloc(1+n, sizeof(int)); |
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| 108 | W->pos = xcalloc(1+n, sizeof(int)); |
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| 109 | memset(&W->pos[1], 0, sizeof(int) * n); |
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| 110 | /* V := 0 */ |
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| 111 | V->size = 0; |
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| 112 | V->list = xcalloc(1+n, sizeof(int)); |
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| 113 | V->pos = xcalloc(1+n, sizeof(int)); |
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| 114 | memset(&V->pos[1], 0, sizeof(int) * n); |
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| 115 | /* main loop */ |
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| 116 | for (i = 1; i <= n; i++) |
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| 117 | { /* W must be empty */ |
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| 118 | xassert(W->size == 0); |
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| 119 | /* W := { j : i > j and (i,j) in E } */ |
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| 120 | len = func(info, i, W->list); |
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| 121 | xassert(0 <= len && len <= n); |
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| 122 | for (t = 1; t <= len; t++) |
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| 123 | { j = W->list[t]; |
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| 124 | xassert(1 <= j && j <= n); |
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| 125 | if (j >= i) continue; |
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| 126 | xassert(W->pos[j] == 0); |
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| 127 | W->list[++W->size] = j, W->pos[j] = W->size; |
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| 128 | } |
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| 129 | /* on i-th iteration we need to cover edges (i,j) for all |
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| 130 | j in W */ |
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| 131 | /* if W is empty, it is a special case */ |
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| 132 | if (W->size == 0) |
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| 133 | { /* set k := k + 1 and create new clique C[k] = { i } */ |
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| 134 | k = glp_add_vertices(H, 1) - n; |
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| 135 | glp_add_arc(H, i, n + k); |
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| 136 | continue; |
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| 137 | } |
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| 138 | /* try to include vertex i into existing cliques */ |
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| 139 | /* V must be empty */ |
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| 140 | xassert(V->size == 0); |
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| 141 | /* k is the number of cliques found so far */ |
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| 142 | k = H->nv - n; |
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| 143 | for (m = 1; m <= k; m++) |
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| 144 | { /* do while V != W; since here V is within W, we can use |
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| 145 | equivalent condition: do while |V| < |W| */ |
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| 146 | if (V->size == W->size) break; |
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| 147 | /* check if C[m] is within W */ |
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| 148 | for (a = H->v[n + m]->in; a != NULL; a = a->h_next) |
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| 149 | { j = a->tail->i; |
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| 150 | if (W->pos[j] == 0) break; |
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| 151 | } |
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| 152 | if (a != NULL) continue; |
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| 153 | /* C[m] is within W, expand clique C[m] with vertex i */ |
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| 154 | /* C[m] := C[m] union {i} */ |
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| 155 | glp_add_arc(H, i, n + m); |
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| 156 | /* V is a set of vertices whose incident edges are already |
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| 157 | covered by existing cliques */ |
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| 158 | /* V := V union C[m] */ |
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| 159 | for (a = H->v[n + m]->in; a != NULL; a = a->h_next) |
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| 160 | { j = a->tail->i; |
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| 161 | if (V->pos[j] == 0) |
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| 162 | V->list[++V->size] = j, V->pos[j] = V->size; |
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| 163 | } |
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| 164 | } |
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| 165 | /* remove from set W the vertices whose incident edges are |
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| 166 | already covered by existing cliques */ |
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| 167 | /* W := W \ V, V := 0 */ |
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| 168 | for (t = 1; t <= V->size; t++) |
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| 169 | { j = V->list[t], V->pos[j] = 0; |
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| 170 | if (W->pos[j] != 0) |
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| 171 | { /* remove vertex j from W */ |
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| 172 | if (W->pos[j] != W->size) |
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| 173 | { int jj = W->list[W->size]; |
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| 174 | W->list[W->pos[j]] = jj; |
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| 175 | W->pos[jj] = W->pos[j]; |
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| 176 | } |
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| 177 | W->size--, W->pos[j] = 0; |
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| 178 | } |
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| 179 | } |
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| 180 | V->size = 0; |
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| 181 | /* now set W contains only vertices whose incident edges are |
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| 182 | still not covered by existing cliques; create new cliques |
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| 183 | to cover remaining edges until set W becomes empty */ |
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| 184 | while (W->size > 0) |
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| 185 | { /* find clique C[m], 1 <= m <= k, which shares maximal |
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| 186 | number of vertices with W; to break ties choose clique |
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| 187 | having smallest number m */ |
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| 188 | m = 0, best = -1; |
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| 189 | k = H->nv - n; |
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| 190 | for (t = 1; t <= k; t++) |
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| 191 | { /* compute cardinality of intersection of W and C[t] */ |
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| 192 | card = 0; |
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| 193 | for (a = H->v[n + t]->in; a != NULL; a = a->h_next) |
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| 194 | { j = a->tail->i; |
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| 195 | if (W->pos[j] != 0) card++; |
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| 196 | } |
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| 197 | if (best < card) |
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| 198 | m = t, best = card; |
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| 199 | } |
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| 200 | xassert(m > 0); |
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| 201 | /* set k := k + 1 and create new clique: |
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| 202 | C[k] := (W intersect C[m]) union { i }, which covers all |
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| 203 | edges incident to vertices from (W intersect C[m]) */ |
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| 204 | k = glp_add_vertices(H, 1) - n; |
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| 205 | for (a = H->v[n + m]->in; a != NULL; a = a->h_next) |
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| 206 | { j = a->tail->i; |
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| 207 | if (W->pos[j] != 0) |
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| 208 | { /* vertex j is in both W and C[m]; include it in new |
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| 209 | clique C[k] */ |
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| 210 | glp_add_arc(H, j, n + k); |
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| 211 | /* remove vertex j from W, since edge (i,j) will be |
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| 212 | covered by new clique C[k] */ |
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| 213 | if (W->pos[j] != W->size) |
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| 214 | { int jj = W->list[W->size]; |
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| 215 | W->list[W->pos[j]] = jj; |
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| 216 | W->pos[jj] = W->pos[j]; |
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| 217 | } |
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| 218 | W->size--, W->pos[j] = 0; |
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| 219 | } |
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| 220 | } |
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| 221 | /* include vertex i to new clique C[k] to cover edges (i,j) |
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| 222 | incident to all vertices j just removed from W */ |
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| 223 | glp_add_arc(H, i, n + k); |
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| 224 | } |
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| 225 | } |
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| 226 | /* free working arrays */ |
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| 227 | xfree(W->list); |
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| 228 | xfree(W->pos); |
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| 229 | xfree(V->list); |
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| 230 | xfree(V->pos); |
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| 231 | /* return the number of cliques in the edge covering found */ |
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| 232 | return H->nv - n; |
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| 233 | } |
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| 234 | |
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| 235 | /* eof */ |
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