src/misc/espresso/mincov.c

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/*
 * Revision Control Information
 *
 * $Source$
 * $Author$
 * $Revision$
 * $Date$
 *
 */
#include "mincov_int.h"

/*
 *  mincov.c
 */

#define USE_GIMPEL
#define USE_INDEP_SET

static int select_column();
static void select_essential();
static int verify_cover();

#define fail(why) {\
    (void) fprintf(stderr, "Fatal error: file %s, line %d\n%s\n",\
        __FILE__, __LINE__, why);\
    (void) fflush(stdout);\
    abort();\
}

sm_row *
sm_minimum_cover(A, weight, heuristic, debug_level)
sm_matrix *A;
int *weight;
int heuristic;          /* set to 1 for a heuristic covering */
int debug_level;        /* how deep in the recursion to provide info */
{
    stats_t stats;
    solution_t *best, *select;
    sm_row *prow, *sol;
    sm_col *pcol;
    sm_matrix *dup_A;
    int nelem, bound;
    double sparsity;

    /* Avoid sillyness */
    if (A->nrows <= 0) {
        return sm_row_alloc();          /* easy to cover */
    }

    /* Initialize debugging structure */
    stats.start_time = util_cpu_time();
    stats.debug = debug_level > 0;
    stats.max_print_depth = debug_level;
    stats.max_depth = -1;
    stats.nodes = 0;
    stats.component = stats.comp_count = 0;
    stats.gimpel = stats.gimpel_count = 0;
    stats.no_branching = heuristic != 0;
    stats.lower_bound = -1;

    /* Check the matrix sparsity */
    nelem = 0;
    sm_foreach_row(A, prow) {
        nelem += prow->length;
    }
    sparsity = (double) nelem / (double) (A->nrows * A->ncols);

    /* Determine an upper bound on the solution */
    bound = 1;
    sm_foreach_col(A, pcol) {
        bound += WEIGHT(weight, pcol->col_num);
    }

    /* Perform the covering */
    select = solution_alloc();
    dup_A = sm_dup(A);
    best = sm_mincov(dup_A, select, weight, 0, bound, 0, &stats);
    sm_free(dup_A);
    solution_free(select);

    if (stats.debug) {
        if (stats.no_branching) {
            (void) printf("**** heuristic covering ...\n");
            (void) printf("lower bound = %d\n", stats.lower_bound);
        }
        (void) printf("matrix     = %d by %d with %d elements (%4.3f%%)\n",
                A->nrows, A->ncols, nelem, sparsity * 100.0);
        (void) printf("cover size = %d elements\n", best->row->length);
        (void) printf("cover cost = %d\n", best->cost);
        (void) printf("time       = %s\n", 
                        util_print_time(util_cpu_time() - stats.start_time));
        (void) printf("components = %d\n", stats.comp_count);
        (void) printf("gimpel     = %d\n", stats.gimpel_count);
        (void) printf("nodes      = %d\n", stats.nodes);
        (void) printf("max_depth  = %d\n", stats.max_depth);
    }

    sol = sm_row_dup(best->row);
    if (! verify_cover(A, sol)) {
        fail("mincov: internal error -- cover verification failed\n");
    }
    solution_free(best);
    return sol;
}

/*
 *  Find the best cover for 'A' (given that 'select' already selected);
 *
 *    - abort search if a solution cannot be found which beats 'bound'
 *
 *    - if any solution meets 'lower_bound', then it is the optimum solution
 *      and can be returned without further work.
 */

solution_t * 
sm_mincov(A, select, weight, lb, bound, depth, stats)
sm_matrix *A;
solution_t *select;
int *weight;
int lb;
int bound;
int depth;
stats_t *stats;
{
    sm_matrix *A1, *A2, *L, *R;
    sm_element *p;
    solution_t *select1, *select2, *best, *best1, *best2, *indep;
    int pick, lb_new, debug;

    /* Start out with some debugging information */
    stats->nodes++;
    if (depth > stats->max_depth) stats->max_depth = depth;
    debug = stats->debug && (depth <= stats->max_print_depth);

    /* Apply row dominance, column dominance, and select essentials */
    select_essential(A, select, weight, bound);
    if (select->cost >= bound) {
        return NIL(solution_t);
    }

    /* See if gimpel's reduction technique applies ... */
#ifdef USE_GIMPEL
    if ( weight == NIL(int)) {  /* hack until we fix it */
        if (gimpel_reduce(A, select, weight, lb, bound, depth, stats, &best)) {
            return best;
        }
    }
#endif

#ifdef USE_INDEP_SET
    /* Determine bound from here to final solution using independent-set */
    indep = sm_maximal_independent_set(A, weight);

    /* make sure the lower bound is monotonically increasing */
    lb_new = MAX(select->cost + indep->cost, lb);
    pick = select_column(A, weight, indep);
    solution_free(indep);
#else
    lb_new = select->cost + (A->nrows > 0);
    pick = select_column(A, weight, NIL(solution_t));
#endif

    if (depth == 0) {
        stats->lower_bound = lb_new + stats->gimpel;
    }

    if (debug) {
        (void) printf("ABSMIN[%2d]%s", depth, stats->component ? "*" : " ");
        (void) printf(" %3dx%3d sel=%3d bnd=%3d lb=%3d %12s ",
            A->nrows, A->ncols, select->cost + stats->gimpel, 
            bound + stats->gimpel, lb_new + stats->gimpel, 
            util_print_time(util_cpu_time()-stats->start_time));
    }

    /* Check for bounding based on no better solution possible */
    if (lb_new >= bound) {
        if (debug) (void) printf("bounded\n");
        best = NIL(solution_t);


    /* Check for new best solution */
    } else if (A->nrows == 0) {
        best = solution_dup(select);
        if (debug) (void) printf("BEST\n");
        if (stats->debug && stats->component == 0) {
            (void) printf("new 'best' solution %d at level %d (time is %s)\n", 
                best->cost + stats->gimpel, depth, 
                util_print_time(util_cpu_time() - stats->start_time));
        }


    /* Check for a partition of the problem */
    } else if (sm_block_partition(A, &L, &R)) {
        /* Make L the smaller problem */
        if (L->ncols > R->ncols) {
            A1 = L;
            L = R;
            R = A1;
        }
        if (debug) (void) printf("comp %d %d\n", L->nrows, R->nrows);
        stats->comp_count++;

        /* Solve problem for L */
        select1 = solution_alloc();
        stats->component++;
        best1 = sm_mincov(L, select1, weight, 0, 
                                    bound-select->cost, depth+1, stats);
        stats->component--;
        solution_free(select1);
        sm_free(L);

        /* Add best solution to the selected set */
        if (best1 == NIL(solution_t)) {
            best = NIL(solution_t);
        } else {
            for(p = best1->row->first_col; p != 0; p = p->next_col) {
                solution_add(select, weight, p->col_num);
            }
            solution_free(best1);

            /* recur for the remaining block */
            best = sm_mincov(R, select, weight, lb_new, bound, depth+1, stats);
        }
        sm_free(R);

    /* We've tried as hard as possible, but now we must split and recur */
    } else {
        if (debug) (void) printf("pick=%d\n", pick);

        /* Assume we choose this column to be in the covering set */
        A1 = sm_dup(A);
        select1 = solution_dup(select);
        solution_accept(select1, A1, weight, pick);
        best1 = sm_mincov(A1, select1, weight, lb_new, bound, depth+1, stats);
        solution_free(select1);
        sm_free(A1);

        /* Update the upper bound if we found a better solution */
        if (best1 != NIL(solution_t) && bound > best1->cost) {
            bound = best1->cost;
        }

        /* See if this is a heuristic covering (no branching) */
        if (stats->no_branching) {
            return best1;
        }

        /* Check for reaching lower bound -- if so, don't actually branch */
        if (best1 != NIL(solution_t) && best1->cost == lb_new) {
            return best1;
        }

        /* Now assume we cannot have that column */
        A2 = sm_dup(A);
        select2 = solution_dup(select);
        solution_reject(select2, A2, weight, pick);
        best2 = sm_mincov(A2, select2, weight, lb_new, bound, depth+1, stats);
        solution_free(select2);
        sm_free(A2);

        best = solution_choose_best(best1, best2);
    }

    return best;
}

static int 
select_column(A, weight, indep)
sm_matrix *A;
int *weight;
solution_t *indep;
{
    register sm_col *pcol;
    register sm_row *prow, *indep_cols;
    register sm_element *p, *p1;
    double w, best;
    int best_col;

    indep_cols = sm_row_alloc();
    if (indep != NIL(solution_t)) {
        /* Find which columns are in the independent sets */
        for(p = indep->row->first_col; p != 0; p = p->next_col) {
            prow = sm_get_row(A, p->col_num);
            for(p1 = prow->first_col; p1 != 0; p1 = p1->next_col) {
                (void) sm_row_insert(indep_cols, p1->col_num);
            }
        }
    } else {
        /* select out of all columns */
        sm_foreach_col(A, pcol) {
            (void) sm_row_insert(indep_cols, pcol->col_num);
        }
    }

    /* Find the best column */
    best_col = -1;
    best = -1;

    /* Consider only columns which are in some independent row */
    sm_foreach_row_element(indep_cols, p1) {
        pcol = sm_get_col(A, p1->col_num);

        /* Compute the total 'value' of all things covered by the column */
        w = 0.0;
        for(p = pcol->first_row; p != 0; p = p->next_row) {
            prow = sm_get_row(A, p->row_num);
            w += 1.0 / ((double) prow->length - 1.0);
        }

        /* divide this by the relative cost of choosing this column */
        w = w / (double) WEIGHT(weight, pcol->col_num);

        /* maximize this ratio */
        if (w  > best) {
            best_col = pcol->col_num;
            best = w;
        }
    }

    sm_row_free(indep_cols);
    return best_col;
}

static void 
select_essential(A, select, weight, bound)
sm_matrix *A;
solution_t *select;
int *weight;
int bound;                      /* must beat this solution */
{
    register sm_element *p;
    register sm_row *prow, *essen;
    int delcols, delrows, essen_count;

    do {
        /*  Check for dominated columns  */
        delcols = sm_col_dominance(A, weight);

        /*  Find the rows with only 1 element (the essentials) */
        essen = sm_row_alloc();
        sm_foreach_row(A, prow) {
            if (prow->length == 1) {
                (void) sm_row_insert(essen, prow->first_col->col_num);
            }
        }

        /* Select all of the elements */
        sm_foreach_row_element(essen, p) {
            solution_accept(select, A, weight, p->col_num);
            /* Make sure solution still looks good */
            if (select->cost >= bound) {
                sm_row_free(essen);
                return;
            }
        }
        essen_count = essen->length;
        sm_row_free(essen);

        /*  Check for dominated rows  */
        delrows = sm_row_dominance(A);

    } while (delcols > 0 || delrows > 0 || essen_count > 0);
}

static int 
verify_cover(A, cover)
sm_matrix *A;
sm_row *cover;
{
    sm_row *prow;

    sm_foreach_row(A, prow) {
        if (! sm_row_intersects(prow, cover)) {
            return 0;
        }
    }
    return 1;
}

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