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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