*
* Invoke as ./main n m
*
- * The algorithm is faster if the arguments are ordered so that n > m.
+ * The arguments must be ordered so that n > m:
+ * n is the number of (more, shorter) input matches of length m
+ * m is the number of (fewer, longer) output matches of length n
*/
/*
#include <unistd.h>
#include <stdbool.h>
#include <inttypes.h>
+#include <math.h>
#include <sys/types.h>
#include <sys/wait.h>
#include <sys/uio.h>
#include <glpk.h>
+#ifndef VERSION
+#define VERSION "(unknown-version)"
+#endif
+
/*
* Algorithm.
*
*
* We search all possible adjacency matrices, and for each one we run
* GLPK's simplex solver. We represent the adjacency matrix as an
- * array of bitmaps.
+ * array of bitmaps: one word per input stick, with one bit per output
+ * stick.
*
* However, there are a couple of wrinkles:
*
* nondecreasing in array order.
*
* Once we have a solution, we also avoid considering any candidate
- * which involves dividing one of the output sticks into so many
+ * which involves dividing one of the input sticks into so many
* fragment that the smallest fragment would necessarily be no bigger
* than our best solution. That is, we reject candidates where any of
* the hamming weights of the adjacency bitmap words are too large.
*
+ * We further winnow the set of possible adjacency matrices, by
+ * ensuring the same bit is not set in too many entries of adjmatrix
+ * (ie, as above, only considering output sticks); and by ensuring
+ * that it is not set in too few: each output stick must consist
+ * of at least two fragments since the output sticks are longer than
+ * the input ones.
+ *
* And, we want to do the search in order of increasing maximum
* hamming weight. This is because in practice optimal solutions tend
* to have low hamming weight, and having found a reasonable solution
typedef uint32_t AdjWord;
#define PRADJ "08"PRIx32
+#define FOR_BITS(j,m) for (j=0, j##bit=1; j < (m); j++, j##bit<<=1)
+
static int n, m, maxhamweight;
static AdjWord *adjmatrix;
static AdjWord adjall;
static glp_prob *best_prob;
static AdjWord *best_adjmatrix;
+static int n_max_frags, m_max_frags;
+static int *weight;
+
static unsigned printcounter;
static void iterate(void);
static void iterate_recurse(int i, AdjWord min);
static bool preconsider_ok(int nwords, bool doprint);
+static bool maxhamweight_ok(void);
static void optimise(bool doprint);
static void progress_eol(void) {
fflush(stderr);
}
+static void set_best(double new_best) {
+ best = new_best;
+ /*
+ * When computing n_max_frags, we want to set a value that will skip
+ * anything that won't provide strictly better solutions. So we
+ * want
+ * frags < n / best
+ * _ _
+ * <=> frags < | n / best |
+ * _ _
+ * <=> frags <= | n / best | - 1
+ *
+ * But best values from glpk are slightly approximate, so we
+ * subtract a fudge factor from our target.
+ */
+ double near_best = best * 0.98 - 0.02;
+ n_max_frags = ceil(n / near_best) - 1;
+ m_max_frags = ceil(m / near_best) - 1;
+}
+
/*----- multicore support -----*/
/*
pid_t pid;
} Worker;
static Worker *mc_us;
+static bool mc_am_generator;
static void multicore_check_for_new_best(void);
-#define MAX_NIOVS 3
+#define MAX_NIOVS 4
static AdjWord mc_iter_min;
static int mc_niovs;
static size_t mc_iovlen;
IOV(maxhamweight, 1);
IOV(mc_iter_min, 1);
IOV(*adjmatrix, multicore_iteration_boundary);
+ IOV(*weight, m);
}
static void mc_rwvsetup_full(void) {
}
static void multicore_outer_iteration(int i, AdjWord min) {
+ static unsigned check_counter;
+
assert(i == multicore_iteration_boundary);
mc_iter_min = min;
mc_rwvsetup_outer();
assert(r == mc_iovlen);
/* effectively, this writev arranges to transfers control
* to some worker's instance of iterate_recurse via mc_iterate_worker */
+
+ if (!(check_counter++ & 0xff))
+ multicore_check_for_new_best();
}
static void mc_iterate_worker(void) {
ssize_t r = readv(mc_work[0], mc_iov, mc_niovs);
if (r == 0) break;
assert(r == mc_iovlen);
+
+ bool ok = maxhamweight_ok();
+ if (!ok) continue;
+
+ ok = preconsider_ok(multicore_iteration_boundary, 1);
+ progress_eol();
+ if (!ok) continue;
/* stop iterate_recurse from trying to run multicore_outer_iteration */
int mc_org_it_bound = multicore_iteration_boundary;
iterate_recurse(mc_org_it_bound, mc_iter_min);
multicore_iteration_boundary = mc_org_it_bound;
}
- LPRINTF("worker %2d reporting",mc_us->w);
if (best_adjmatrix) {
+ LPRINTF("worker %2d reporting",mc_us->w);
adjmatrix = best_adjmatrix;
mc_rwvsetup_full();
ssize_t r = writev(fileno(mc_us->results), mc_iov, mc_niovs);
genpid = fork(); assert(genpid >= 0);
if (!genpid) {
+ mc_am_generator = 1;
LPRINTF("generator running");
iterate();
exit(0);
LPRINTF("reading report from %2d",w);
ssize_t sr = preadv(fileno(mc_workers[w].results), mc_iov, mc_niovs, 0);
if (!sr) continue;
+ LPRINTF("got report from %2d",w);
maxhamweight = 0;
optimise(1);
}
}
static void multicore_check_for_new_best(void) {
- if (!ncpus) return;
+ if (!(mc_us || mc_am_generator))
+ return;
for (;;) {
double msg;
if (!got) break;
assert(got == sizeof(msg));
if (msg > best)
- best = msg;
+ set_best(msg);
mc_bus_read += sizeof(msg);
}
}
static void multicore_found_new_best(void) {
- if (!ncpus) return;
+ if (!mc_us)
+ return;
if (mc_us /* might be master */) fprintf(stderr," w%-2d ",mc_us->w);
ssize_t wrote = write(mc_bus, &best, sizeof(best));
adjmatrix = xalloc_adjmatrix();
glp_term_out(GLP_OFF);
setlinebuf(stderr);
+ weight = calloc(sizeof(*weight), m); assert(weight);
+ n_max_frags = INT_MAX;
+ m_max_frags = INT_MAX;
}
+#if 0
static AdjWord one_adj_bit(int bitnum) {
return (AdjWord)1 << bitnum;
}
+#endif
static int count_set_adj_bits(AdjWord w) {
- int j, total;
- for (j=0, total=0; j<m; j++)
- total += !!(w & one_adj_bit(j));
+ int j, total = 0;
+ AdjWord jbit;
+ FOR_BITS(j,m)
+ total += !!(w & jbit);
return total;
}
static int totalfrags;
+static bool maxhamweight_ok(void) {
+ return maxhamweight <= m_max_frags;
+}
+
static bool preconsider_ok(int nwords, bool doprint) {
int i;
bool had_max = 0;
for (i=0, totalfrags=0; i<nwords; i++) {
int frags = count_set_adj_bits(adjmatrix[i]);
- had_max += (frags >= maxhamweight);
- totalfrags += frags;
PRINTF("%"PRADJ" ", adjmatrix[i]);
- double maxminsize = (double)m / frags;
- if (maxminsize <= best) {
+ if (frags > m_max_frags) {
PRINTF(" too fine");
goto out;
}
+ had_max += (frags >= maxhamweight);
+ totalfrags += frags;
}
if (!had_max) {
/* Skip this candidate as its max hamming weight is lower than
/* Consider the best answer (if any) for a given adjacency matrix */
glp_prob *prob = 0;
int i, j;
+ AdjWord jbit;
/*
* Up to a certain point, optimise() can be restarted. We use this
glp_set_obj_coef(prob, X_minimum, 1);
for (i=0; i<n; i++) {
- for (j=0; j<m; j++) {
- if (!(adjmatrix[i] & one_adj_bit(j)))
+ FOR_BITS(j,m) {
+ if (!(adjmatrix[i] & jbit))
continue;
/* x_total_i += x_minimum */
/* x_total_j += x_minimum */
HAVE_PRINTED;
- best = got;
+ set_best(got);
multicore_found_new_best();
if (best_prob) glp_delete_prob(best_prob);
}
static void iterate_recurse(int i, AdjWord min) {
+ int j;
+ AdjWord jbit;
+
if (i >= n) {
+ for (j=0; j<m; j++)
+ if (weight[j] < 2)
+ return;
+
printcounter++;
optimise(!(printcounter & 0xfff));
return;
if (i == 0 && (adjmatrix[i] & (1+adjmatrix[i])))
goto again;
+ FOR_BITS(j,m)
+ if (adjmatrix[i] & jbit)
+ weight[j]++;
+ for (int j = 0; j < m; j++)
+ if (weight[j] >= n_max_frags)
+ goto takeout;
+
iterate_recurse(i+1, adjmatrix[i]);
+ takeout:
+ FOR_BITS(j,m)
+ if (adjmatrix[i] & jbit)
+ weight[j]--;
+
again:
if (adjmatrix[i] == adjall)
return;
static void iterate(void) {
for (maxhamweight=1; maxhamweight<=m; maxhamweight++) {
- double maxminsize = (double)m / maxhamweight;
- if (maxminsize <= best)
+ if (!maxhamweight_ok())
continue;
iterate_recurse(0, 1);
continue;
a[x][y] = min + glp_get_col_prim(best_prob, i);
}
- printf("%d into %d: min fragment %g\n", n, m, min);
+ printf("%d into %d: min fragment %g [%s]\n", n, m, min, VERSION);
for (i = 0; i < n; i++) {
for (j = 0; j < m; j++) {
if (a[i][j])
assert(argc==3);
n = atoi(argv[1]);
m = atoi(argv[2]);
+ assert(n > m);
prep();
~ianmdlvl / matchsticks-search.git / blobdiff