lemon-project-template-glpk
view deps/glpk/src/glpnet09.c @ 9:33de93886c88
Import GLPK 4.47
| author | Alpar Juttner <alpar@cs.elte.hu> |
|---|---|
| date | Sun, 06 Nov 2011 20:59:10 +0100 |
| parents | |
| children |
line source
1 /* glpnet09.c */
3 /***********************************************************************
4 * This code is part of GLPK (GNU Linear Programming Kit).
5 *
6 * Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,
7 * 2009, 2010, 2011 Andrew Makhorin, Department for Applied Informatics,
8 * Moscow Aviation Institute, Moscow, Russia. All rights reserved.
9 * E-mail: <mao@gnu.org>.
10 *
11 * GLPK is free software: you can redistribute it and/or modify it
12 * under the terms of the GNU General Public License as published by
13 * the Free Software Foundation, either version 3 of the License, or
14 * (at your option) any later version.
15 *
16 * GLPK is distributed in the hope that it will be useful, but WITHOUT
17 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
18 * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
19 * License for more details.
20 *
21 * You should have received a copy of the GNU General Public License
22 * along with GLPK. If not, see <http://www.gnu.org/licenses/>.
23 ***********************************************************************/
25 #include "glpapi.h"
26 #include "glpnet.h"
28 /***********************************************************************
29 * NAME
30 *
31 * kellerman - cover edges by cliques with Kellerman's heuristic
32 *
33 * SYNOPSIS
34 *
35 * #include "glpnet.h"
36 * int kellerman(int n, int (*func)(void *info, int i, int ind[]),
37 * void *info, glp_graph *H);
38 *
39 * DESCRIPTION
40 *
41 * The routine kellerman implements Kellerman's heuristic algorithm
42 * to find a minimal set of cliques which cover all edges of specified
43 * graph G = (V, E).
44 *
45 * The parameter n specifies the number of vertices |V|, n >= 0.
46 *
47 * Formal routine func specifies the set of edges E in the following
48 * way. Running the routine kellerman calls the routine func and passes
49 * to it parameter i, which is the number of some vertex, 1 <= i <= n.
50 * In response the routine func should store numbers of all vertices
51 * adjacent to vertex i to locations ind[1], ind[2], ..., ind[len] and
52 * return the value of len, which is the number of adjacent vertices,
53 * 0 <= len <= n. Self-loops are allowed, but ignored. Multiple edges
54 * are not allowed.
55 *
56 * The parameter info is a transit pointer (magic cookie) passed to the
57 * formal routine func as its first parameter.
58 *
59 * The result provided by the routine kellerman is the bipartite graph
60 * H = (V union C, F), which defines the covering found. (The program
61 * object of type glp_graph specified by the parameter H should be
62 * previously created with the routine glp_create_graph. On entry the
63 * routine kellerman erases the content of this object with the routine
64 * glp_erase_graph.) Vertices of first part V correspond to vertices of
65 * the graph G and have the same ordinal numbers 1, 2, ..., n. Vertices
66 * of second part C correspond to cliques and have ordinal numbers
67 * n+1, n+2, ..., n+k, where k is the total number of cliques in the
68 * edge covering found. Every edge f in F in the program object H is
69 * represented as arc f = (i->j), where i in V and j in C, which means
70 * that vertex i of the graph G is in clique C[j], 1 <= j <= k. (Thus,
71 * if two vertices of the graph G are in the same clique, these vertices
72 * are adjacent in G, and corresponding edge is covered by that clique.)
73 *
74 * RETURNS
75 *
76 * The routine Kellerman returns k, the total number of cliques in the
77 * edge covering found.
78 *
79 * REFERENCE
80 *
81 * For more details see: glpk/doc/notes/keller.pdf (in Russian). */
83 struct set
84 { /* set of vertices */
85 int size;
86 /* size (cardinality) of the set, 0 <= card <= n */
87 int *list; /* int list[1+n]; */
88 /* the set contains vertices list[1,...,size] */
89 int *pos; /* int pos[1+n]; */
90 /* pos[i] > 0 means that vertex i is in the set and
91 list[pos[i]] = i; pos[i] = 0 means that vertex i is not in
92 the set */
93 };
95 int kellerman(int n, int (*func)(void *info, int i, int ind[]),
96 void *info, void /* glp_graph */ *H_)
97 { glp_graph *H = H_;
98 struct set W_, *W = &W_, V_, *V = &V_;
99 glp_arc *a;
100 int i, j, k, m, t, len, card, best;
101 xassert(n >= 0);
102 /* H := (V, 0; 0), where V is the set of vertices of graph G */
103 glp_erase_graph(H, H->v_size, H->a_size);
104 glp_add_vertices(H, n);
105 /* W := 0 */
106 W->size = 0;
107 W->list = xcalloc(1+n, sizeof(int));
108 W->pos = xcalloc(1+n, sizeof(int));
109 memset(&W->pos[1], 0, sizeof(int) * n);
110 /* V := 0 */
111 V->size = 0;
112 V->list = xcalloc(1+n, sizeof(int));
113 V->pos = xcalloc(1+n, sizeof(int));
114 memset(&V->pos[1], 0, sizeof(int) * n);
115 /* main loop */
116 for (i = 1; i <= n; i++)
117 { /* W must be empty */
118 xassert(W->size == 0);
119 /* W := { j : i > j and (i,j) in E } */
120 len = func(info, i, W->list);
121 xassert(0 <= len && len <= n);
122 for (t = 1; t <= len; t++)
123 { j = W->list[t];
124 xassert(1 <= j && j <= n);
125 if (j >= i) continue;
126 xassert(W->pos[j] == 0);
127 W->list[++W->size] = j, W->pos[j] = W->size;
128 }
129 /* on i-th iteration we need to cover edges (i,j) for all
130 j in W */
131 /* if W is empty, it is a special case */
132 if (W->size == 0)
133 { /* set k := k + 1 and create new clique C[k] = { i } */
134 k = glp_add_vertices(H, 1) - n;
135 glp_add_arc(H, i, n + k);
136 continue;
137 }
138 /* try to include vertex i into existing cliques */
139 /* V must be empty */
140 xassert(V->size == 0);
141 /* k is the number of cliques found so far */
142 k = H->nv - n;
143 for (m = 1; m <= k; m++)
144 { /* do while V != W; since here V is within W, we can use
145 equivalent condition: do while |V| < |W| */
146 if (V->size == W->size) break;
147 /* check if C[m] is within W */
148 for (a = H->v[n + m]->in; a != NULL; a = a->h_next)
149 { j = a->tail->i;
150 if (W->pos[j] == 0) break;
151 }
152 if (a != NULL) continue;
153 /* C[m] is within W, expand clique C[m] with vertex i */
154 /* C[m] := C[m] union {i} */
155 glp_add_arc(H, i, n + m);
156 /* V is a set of vertices whose incident edges are already
157 covered by existing cliques */
158 /* V := V union C[m] */
159 for (a = H->v[n + m]->in; a != NULL; a = a->h_next)
160 { j = a->tail->i;
161 if (V->pos[j] == 0)
162 V->list[++V->size] = j, V->pos[j] = V->size;
163 }
164 }
165 /* remove from set W the vertices whose incident edges are
166 already covered by existing cliques */
167 /* W := W \ V, V := 0 */
168 for (t = 1; t <= V->size; t++)
169 { j = V->list[t], V->pos[j] = 0;
170 if (W->pos[j] != 0)
171 { /* remove vertex j from W */
172 if (W->pos[j] != W->size)
173 { int jj = W->list[W->size];
174 W->list[W->pos[j]] = jj;
175 W->pos[jj] = W->pos[j];
176 }
177 W->size--, W->pos[j] = 0;
178 }
179 }
180 V->size = 0;
181 /* now set W contains only vertices whose incident edges are
182 still not covered by existing cliques; create new cliques
183 to cover remaining edges until set W becomes empty */
184 while (W->size > 0)
185 { /* find clique C[m], 1 <= m <= k, which shares maximal
186 number of vertices with W; to break ties choose clique
187 having smallest number m */
188 m = 0, best = -1;
189 k = H->nv - n;
190 for (t = 1; t <= k; t++)
191 { /* compute cardinality of intersection of W and C[t] */
192 card = 0;
193 for (a = H->v[n + t]->in; a != NULL; a = a->h_next)
194 { j = a->tail->i;
195 if (W->pos[j] != 0) card++;
196 }
197 if (best < card)
198 m = t, best = card;
199 }
200 xassert(m > 0);
201 /* set k := k + 1 and create new clique:
202 C[k] := (W intersect C[m]) union { i }, which covers all
203 edges incident to vertices from (W intersect C[m]) */
204 k = glp_add_vertices(H, 1) - n;
205 for (a = H->v[n + m]->in; a != NULL; a = a->h_next)
206 { j = a->tail->i;
207 if (W->pos[j] != 0)
208 { /* vertex j is in both W and C[m]; include it in new
209 clique C[k] */
210 glp_add_arc(H, j, n + k);
211 /* remove vertex j from W, since edge (i,j) will be
212 covered by new clique C[k] */
213 if (W->pos[j] != W->size)
214 { int jj = W->list[W->size];
215 W->list[W->pos[j]] = jj;
216 W->pos[jj] = W->pos[j];
217 }
218 W->size--, W->pos[j] = 0;
219 }
220 }
221 /* include vertex i to new clique C[k] to cover edges (i,j)
222 incident to all vertices j just removed from W */
223 glp_add_arc(H, i, n + k);
224 }
225 }
226 /* free working arrays */
227 xfree(W->list);
228 xfree(W->pos);
229 xfree(V->list);
230 xfree(V->pos);
231 /* return the number of cliques in the edge covering found */
232 return H->nv - n;
233 }
235 /* eof */