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/***********************************************************************
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* This code is part of GLPK (GNU Linear Programming Kit).
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* Two subroutines sub() and wclique() below are intended to find a
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* maximum weight clique in a given undirected graph. These subroutines
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* are slightly modified version of the program WCLIQUE developed by
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* Patric Ostergard <http://www.tcs.hut.fi/~pat/wclique.html> and based
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* on ideas from the article "P. R. J. Ostergard, A new algorithm for
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* the maximum-weight clique problem, submitted for publication", which
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* in turn is a generalization of the algorithm for unweighted graphs
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* presented in "P. R. J. Ostergard, A fast algorithm for the maximum
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* clique problem, submitted for publication".
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* USED WITH PERMISSION OF THE AUTHOR OF THE ORIGINAL CODE.
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* Changes were made by Andrew Makhorin <mao@gnu.org>.
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* GLPK is free software: you can redistribute it and/or modify it
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* under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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* GLPK is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
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* License for more details.
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* You should have received a copy of the GNU General Public License
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* along with GLPK. If not, see <http://www.gnu.org/licenses/>.
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***********************************************************************/
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/***********************************************************************
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* wclique - find maximum weight clique with Ostergard's algorithm
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* int wclique(int n, const int w[], const unsigned char a[],
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* The routine wclique finds a maximum weight clique in an undirected
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* graph with Ostergard's algorithm.
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* n is the number of vertices, n > 0.
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* w[i], i = 1,...,n, is a weight of vertex i.
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* a[*] is the strict (without main diagonal) lower triangle of the
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* graph adjacency matrix in packed format.
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* ind[k], k = 1,...,size, is the number of a vertex included in the
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* clique found, 1 <= ind[k] <= n, where size is the number of vertices
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* in the clique returned on exit.
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* The routine returns the clique size, i.e. the number of vertices in
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{ /* common storage area */
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/* number of vertices */
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const int *wt; /* int wt[0:n-1]; */
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const unsigned char *a;
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/* adjacency matrix (packed lower triangle without main diag.) */
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/* weight of best clique */
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/* number of vertices in best clique */
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int *rec; /* int rec[0:n-1]; */
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/* best clique so far */
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int *clique; /* int clique[0:n-1]; */
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/* table for pruning */
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int *set; /* int set[0:n-1]; */
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#define record (csa->record)
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#define rec_level (csa->rec_level)
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#define rec (csa->rec)
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#define clique (csa->clique)
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#define set (csa->set)
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static int is_edge(struct csa *csa, int i, int j)
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{ /* if there is arc (i,j), the routine returns true; otherwise
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false; 0 <= i, j < n */
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xassert(0 <= i && i < n);
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xassert(0 <= j && j < n);
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if (i == j) return 0;
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if (i < j) k = i, i = j, j = k;
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k = (i * (i - 1)) / 2 + j;
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return a[k / CHAR_BIT] &
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(unsigned char)(1 << ((CHAR_BIT - 1) - k % CHAR_BIT));
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#define is_edge(csa, i, j) ((i) == (j) ? 0 : \
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(i) > (j) ? is_edge1(i, j) : is_edge1(j, i))
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#define is_edge1(i, j) is_edge2(((i) * ((i) - 1)) / 2 + (j))
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#define is_edge2(k) (a[(k) / CHAR_BIT] & \
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(unsigned char)(1 << ((CHAR_BIT - 1) - (k) % CHAR_BIT)))
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static void sub(struct csa *csa, int ct, int table[], int level,
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int weight, int l_weight)
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{ int i, j, k, curr_weight, left_weight, *p1, *p2, *newtable;
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newtable = xcalloc(n, sizeof(int));
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{ /* 0 or 1 elements left; include these */
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{ set[level++] = table[0];
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for (i = 0; i < level; i++) rec[i] = set[i];
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for (i = ct; i >= 0; i--)
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{ if ((level == 0) && (i < ct)) goto done;
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if ((level > 0) && (clique[k] <= (record - weight)))
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goto done; /* prune */
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curr_weight = weight + wt[k];
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if (l_weight <= (record - curr_weight))
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goto done; /* prune */
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while (p2 < table + i)
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if (is_edge(csa, j, k))
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left_weight += wt[j];
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if (left_weight <= (record - curr_weight)) continue;
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sub(csa, p1 - newtable - 1, newtable, level + 1, curr_weight,
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done: xfree(newtable);
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int wclique(int _n, const int w[], const unsigned char _a[], int ind[])
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{ struct csa _csa, *csa = &_csa;
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int i, j, p, max_wt, max_nwt, wth, *used, *nwt, *pos;
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clique = xcalloc(n, sizeof(int));
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set = xcalloc(n, sizeof(int));
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used = xcalloc(n, sizeof(int));
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nwt = xcalloc(n, sizeof(int));
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pos = xcalloc(n, sizeof(int));
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for (i = 0; i < n; i++)
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for (j = 0; j < n; j++)
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if (is_edge(csa, i, j)) nwt[i] += wt[j];
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for (i = 0; i < n; i++)
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for (i = n-1; i >= 0; i--)
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for (j = 0; j < n; j++)
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{ if ((!used[j]) && ((wt[j] > max_wt) || (wt[j] == max_wt
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&& nwt[j] > max_nwt)))
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for (j = 0; j < n; j++)
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if ((!used[j]) && (j != p) && (is_edge(csa, p, j)))
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for (i = 0; i < n; i++)
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sub(csa, i, pos, 0, 0, wth);
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clique[pos[i]] = record;
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if (xdifftime(xtime(), timer) >= 5.0 - 0.001)
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{ /* print current record and reset timer */
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xprintf("level = %d (%d); best = %d\n", i+1, n, record);
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/* return the solution found */
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for (i = 1; i <= rec_level; i++) ind[i]++;
added
removed
optional/glpk/glpnet08.c
