static int find_clique(struct csa *csa, int c_ind[])
{ /* find maximum weight clique in induced subgraph with exact
* Ostergard's algorithm */
int nn = csa->nn;
double *wgt = csa->wgt;
int i, j, k, p, q, t, ne, nb, len, *iwt, *ind;
unsigned char *a;
xassert(nn >= 2);
/* allocate working array */
ind = talloc(1+nn, int);
/* calculate the number of elements in lower triangle (without
* diagonal) of adjacency matrix of induced subgraph */
ne = (nn * (nn - 1)) / 2;
/* calculate the number of bytes needed to store lower triangle
* of adjacency matrix */
nb = (ne + (CHAR_BIT - 1)) / CHAR_BIT;
/* allocate lower triangle of adjacency matrix */
a = talloc(nb, unsigned char);
/* fill lower triangle of adjacency matrix */
memset(a, 0, nb);
for (p = 1; p <= nn; p++)
{ /* retrieve vertices adjacent to vertex p */
len = sub_adjacent(csa, p, ind);
for (k = 1; k <= len; k++)
{ /* there exists edge (p, q) in induced subgraph */
q = ind[k];
xassert(1 <= q && q <= nn && q != p);
/* determine row and column indices of this edge in lower
* triangle of adjacency matrix */
if (p > q)
i = p, j = q;
else /* p < q */
i = q, j = p;
/* set bit a[i,j] to 1, i > j */
t = ((i - 1) * (i - 2)) / 2 + (j - 1);
a[t / CHAR_BIT] |=
(unsigned char)(1 << ((CHAR_BIT - 1) - t % CHAR_BIT));
}
}
/* scale vertex weights by 1000 and convert them to integers as
* required by Ostergard's algorithm */
iwt = ind;
for (i = 1; i <= nn; i++)
{ /* it is assumed that 0 <= wgt[i] <= 1 */
t = (int)(1000.0 * wgt[i] + 0.5);
if (t < 0)
t = 0;
else if (t > 1000)
t = 1000;
iwt[i] = t;
}
/* find maximum weight clique */
len = wclique(nn, iwt, a, c_ind);
/* free working arrays */
tfree(ind);
tfree(a);
/* return clique size to calling routine */
return len;
}
int scg_max_clique(SCG *g, const int w[], int list[])
{ int size;
if (g->n == 0)
size = 0;
else
size = wclique(g, w, list);
return size;
}
int glp_wclique_exact(glp_graph *G, int v_wgt, double *sol, int v_set)
{ /* find maximum weight clique with exact algorithm */
glp_arc *e;
int i, j, k, len, x, *w, *ind, ret = 0;
unsigned char *a;
double s, t;
if (v_wgt >= 0 && v_wgt > G->v_size - (int)sizeof(double))
xerror("glp_wclique_exact: v_wgt = %d; invalid parameter\n",
v_wgt);
if (v_set >= 0 && v_set > G->v_size - (int)sizeof(int))
xerror("glp_wclique_exact: v_set = %d; invalid parameter\n",
v_set);
if (G->nv == 0)
{ /* empty graph has only empty clique */
if (sol != NULL) *sol = 0.0;
return 0;
}
/* allocate working arrays */
w = xcalloc(1+G->nv, sizeof(int));
ind = xcalloc(1+G->nv, sizeof(int));
len = G->nv; /* # vertices */
len = len * (len - 1) / 2; /* # entries in lower triangle */
len = (len + (CHAR_BIT - 1)) / CHAR_BIT; /* # bytes needed */
a = xcalloc(len, sizeof(char));
memset(a, 0, len * sizeof(char));
/* determine vertex weights */
s = 0.0;
for (i = 1; i <= G->nv; i++)
{ if (v_wgt >= 0)
{ memcpy(&t, (char *)G->v[i]->data + v_wgt, sizeof(double));
if (!(0.0 <= t && t <= (double)INT_MAX && t == floor(t)))
{ ret = GLP_EDATA;
goto done;
}
w[i] = (int)t;
}
else
w[i] = 1;
s += (double)w[i];
}
if (s > (double)INT_MAX)
{ ret = GLP_EDATA;
goto done;
}
/* build the adjacency matrix */
for (i = 1; i <= G->nv; i++)
{ for (e = G->v[i]->in; e != NULL; e = e->h_next)
{ j = e->tail->i;
/* there exists edge (j,i) in the graph */
if (i > j) set_edge(G->nv, a, i, j);
}
for (e = G->v[i]->out; e != NULL; e = e->t_next)
{ j = e->head->i;
/* there exists edge (i,j) in the graph */
if (i > j) set_edge(G->nv, a, i, j);
}
}
/* find maximum weight clique in the graph */
len = wclique(G->nv, w, a, ind);
/* compute the clique weight */
s = 0.0;
for (k = 1; k <= len; k++)
{ i = ind[k];
xassert(1 <= i && i <= G->nv);
s += (double)w[i];
}
if (sol != NULL) *sol = s;
/* mark vertices included in the clique */
if (v_set >= 0)
{ x = 0;
for (i = 1; i <= G->nv; i++)
memcpy((char *)G->v[i]->data + v_set, &x, sizeof(int));
x = 1;
for (k = 1; k <= len; k++)
{ i = ind[k];
memcpy((char *)G->v[i]->data + v_set, &x, sizeof(int));
}
}
done: /* free working arrays */
xfree(w);
xfree(ind);
xfree(a);
return ret;
}
int lpx_clique_cut(LPX *lp, void *_cog, int ind[], double val[])
{ struct COG *cog = _cog;
int n = lpx_get_num_cols(lp);
int j, t, v, card, temp, len = 0, *w, *sol;
double x, sum, b, *vec;
/* allocate working arrays */
w = xcalloc(1 + 2 * cog->nb, sizeof(int));
sol = xcalloc(1 + 2 * cog->nb, sizeof(int));
vec = xcalloc(1+n, sizeof(double));
/* assign weights to vertices of the conflict graph */
for (t = 1; t <= cog->nb; t++)
{ j = cog->orig[t];
x = lpx_get_col_prim(lp, j);
temp = (int)(100.0 * x + 0.5);
if (temp < 0) temp = 0;
if (temp > 100) temp = 100;
w[t] = temp;
w[cog->nb + t] = 100 - temp;
}
/* find a clique of maximum weight */
card = wclique(2 * cog->nb, w, cog->a, sol);
/* compute the clique weight for unscaled values */
sum = 0.0;
for ( t = 1; t <= card; t++)
{ v = sol[t];
xassert(1 <= v && v <= 2 * cog->nb);
if (v <= cog->nb)
{ /* vertex v corresponds to binary variable x[j] */
j = cog->orig[v];
x = lpx_get_col_prim(lp, j);
sum += x;
}
else
{ /* vertex v corresponds to the complement of x[j] */
j = cog->orig[v - cog->nb];
x = lpx_get_col_prim(lp, j);
sum += 1.0 - x;
}
}
/* if the sum of binary variables and their complements in the
clique greater than 1, the clique cut is violated */
if (sum >= 1.01)
{ /* construct the inquality */
for (j = 1; j <= n; j++) vec[j] = 0;
b = 1.0;
for (t = 1; t <= card; t++)
{ v = sol[t];
if (v <= cog->nb)
{ /* vertex v corresponds to binary variable x[j] */
j = cog->orig[v];
xassert(1 <= j && j <= n);
vec[j] += 1.0;
}
else
{ /* vertex v corresponds to the complement of x[j] */
j = cog->orig[v - cog->nb];
xassert(1 <= j && j <= n);
vec[j] -= 1.0;
b -= 1.0;
}
}
xassert(len == 0);
for (j = 1; j <= n; j++)
{ if (vec[j] != 0.0)
{ len++;
ind[len] = j, val[len] = vec[j];
}
}
ind[0] = 0, val[0] = b;
}
/* free working arrays */
xfree(w);
xfree(sol);
xfree(vec);
/* return to the calling program */
return len;
}
