1 | /* glpapi18.c (maximum clique problem) */ |
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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 | static void set_edge(int nv, unsigned char a[], int i, int j) |
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29 | { int k; |
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30 | xassert(1 <= j && j < i && i <= nv); |
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31 | k = ((i - 1) * (i - 2)) / 2 + (j - 1); |
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32 | a[k / CHAR_BIT] |= |
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33 | (unsigned char)(1 << ((CHAR_BIT - 1) - k % CHAR_BIT)); |
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34 | return; |
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35 | } |
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36 | |
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37 | int glp_wclique_exact(glp_graph *G, int v_wgt, double *sol, int v_set) |
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38 | { /* find maximum weight clique with exact algorithm */ |
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39 | glp_arc *e; |
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40 | int i, j, k, len, x, *w, *ind, ret = 0; |
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41 | unsigned char *a; |
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42 | double s, t; |
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43 | if (v_wgt >= 0 && v_wgt > G->v_size - (int)sizeof(double)) |
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44 | xerror("glp_wclique_exact: v_wgt = %d; invalid parameter\n", |
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45 | v_wgt); |
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46 | if (v_set >= 0 && v_set > G->v_size - (int)sizeof(int)) |
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47 | xerror("glp_wclique_exact: v_set = %d; invalid parameter\n", |
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48 | v_set); |
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49 | if (G->nv == 0) |
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50 | { /* empty graph has only empty clique */ |
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51 | if (sol != NULL) *sol = 0.0; |
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52 | return 0; |
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53 | } |
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54 | /* allocate working arrays */ |
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55 | w = xcalloc(1+G->nv, sizeof(int)); |
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56 | ind = xcalloc(1+G->nv, sizeof(int)); |
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57 | len = G->nv; /* # vertices */ |
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58 | len = len * (len - 1) / 2; /* # entries in lower triangle */ |
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59 | len = (len + (CHAR_BIT - 1)) / CHAR_BIT; /* # bytes needed */ |
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60 | a = xcalloc(len, sizeof(char)); |
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61 | memset(a, 0, len * sizeof(char)); |
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62 | /* determine vertex weights */ |
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63 | s = 0.0; |
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64 | for (i = 1; i <= G->nv; i++) |
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65 | { if (v_wgt >= 0) |
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66 | { memcpy(&t, (char *)G->v[i]->data + v_wgt, sizeof(double)); |
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67 | if (!(0.0 <= t && t <= (double)INT_MAX && t == floor(t))) |
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68 | { ret = GLP_EDATA; |
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69 | goto done; |
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70 | } |
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71 | w[i] = (int)t; |
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72 | } |
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73 | else |
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74 | w[i] = 1; |
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75 | s += (double)w[i]; |
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76 | } |
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77 | if (s > (double)INT_MAX) |
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78 | { ret = GLP_EDATA; |
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79 | goto done; |
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80 | } |
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81 | /* build the adjacency matrix */ |
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82 | for (i = 1; i <= G->nv; i++) |
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83 | { for (e = G->v[i]->in; e != NULL; e = e->h_next) |
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84 | { j = e->tail->i; |
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85 | /* there exists edge (j,i) in the graph */ |
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86 | if (i > j) set_edge(G->nv, a, i, j); |
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87 | } |
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88 | for (e = G->v[i]->out; e != NULL; e = e->t_next) |
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89 | { j = e->head->i; |
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90 | /* there exists edge (i,j) in the graph */ |
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91 | if (i > j) set_edge(G->nv, a, i, j); |
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92 | } |
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93 | } |
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94 | /* find maximum weight clique in the graph */ |
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95 | len = wclique(G->nv, w, a, ind); |
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96 | /* compute the clique weight */ |
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97 | s = 0.0; |
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98 | for (k = 1; k <= len; k++) |
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99 | { i = ind[k]; |
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100 | xassert(1 <= i && i <= G->nv); |
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101 | s += (double)w[i]; |
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102 | } |
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103 | if (sol != NULL) *sol = s; |
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104 | /* mark vertices included in the clique */ |
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105 | if (v_set >= 0) |
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106 | { x = 0; |
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107 | for (i = 1; i <= G->nv; i++) |
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108 | memcpy((char *)G->v[i]->data + v_set, &x, sizeof(int)); |
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109 | x = 1; |
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110 | for (k = 1; k <= len; k++) |
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111 | { i = ind[k]; |
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112 | memcpy((char *)G->v[i]->data + v_set, &x, sizeof(int)); |
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113 | } |
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114 | } |
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115 | done: /* free working arrays */ |
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116 | xfree(w); |
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117 | xfree(ind); |
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118 | xfree(a); |
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119 | return ret; |
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120 | } |
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121 | |
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122 | /* eof */ |
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