X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ianmdlvl/git?p=matchsticks-search.git;a=blobdiff_plain;f=main.c;h=fb270e0d75ccf61d6f07917a5e432b37860fe409;hp=3fa6ad3a0257d7087de5fe39a88bd665e59b00d2;hb=0fcf88703f2713fdee86521788dcda30f82cb8ff;hpb=33c2116932d26da928f87e70cb16c97358d8bf0c

diff --git a/main.c b/main.c
index 3fa6ad3..fb270e0 100644
--- a/main.c
+++ b/main.c
@@ -5,7 +5,13 @@
  *
  * 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
+ *
+ * Options:
+ *  -j<jobs>     run in parallel on <jobs> cores
+ *  -b<best>     search only for better than <best>
  */
 
 /*
@@ -58,7 +64,8 @@
  *
  * 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:
  *
@@ -76,11 +83,18 @@
  * 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
@@ -91,6 +105,8 @@
 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;
@@ -99,7 +115,7 @@ static double best;
 static glp_prob *best_prob;
 static AdjWord *best_adjmatrix;
 
-static int n_over_best;
+static int n_max_frags, m_max_frags;
 static int *weight;
 
 static unsigned printcounter;
@@ -117,7 +133,22 @@ static void progress_eol(void) {
 
 static void set_best(double new_best) {
   best = new_best;
-  n_over_best = floor(n / 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 -----*/
@@ -159,6 +190,7 @@ typedef struct {
   pid_t pid;
 } Worker;
 static Worker *mc_us;
+static bool mc_am_generator;
 
 static void multicore_check_for_new_best(void);
 
@@ -250,8 +282,8 @@ static void mc_iterate_worker(void) {
     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);
@@ -294,6 +326,7 @@ static void multicore(void) {
 
   genpid = fork();  assert(genpid >= 0);
   if (!genpid) {
+    mc_am_generator = 1;
     LPRINTF("generator running");
     iterate();
     exit(0);
@@ -309,13 +342,15 @@ static void multicore(void) {
     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;
@@ -329,7 +364,8 @@ static void multicore_check_for_new_best(void) {
 }
 
 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));
@@ -348,17 +384,21 @@ static void prep(void) {
   glp_term_out(GLP_OFF);
   setlinebuf(stderr);
   weight = calloc(sizeof(*weight), m);  assert(weight);
-  n_over_best = INT_MAX;
+  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;
 }
 
@@ -367,8 +407,7 @@ static int count_set_adj_bits(AdjWord w) {
 static int totalfrags;
 
 static bool maxhamweight_ok(void) {
-  double maxminsize = (double)m / maxhamweight;
-  return maxminsize > best;
+  return maxhamweight <= m_max_frags;
 }
 
 static bool preconsider_ok(int nwords, bool doprint) {
@@ -379,14 +418,13 @@ static bool preconsider_ok(int nwords, bool doprint) {
   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
@@ -406,6 +444,7 @@ static void optimise(bool doprint) {
   /* 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
@@ -491,8 +530,8 @@ static void optimise(bool doprint) {
   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 */
@@ -593,7 +632,14 @@ static void optimise(bool doprint) {
 }
 
 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;
@@ -610,18 +656,18 @@ static void iterate_recurse(int i, AdjWord min) {
     if (i == 0 && (adjmatrix[i] & (1+adjmatrix[i])))
       goto again;
 
-    for (int j = 0; j < m; j++)
-      if (adjmatrix[i] & one_adj_bit(j))
+    FOR_BITS(j,m)
+      if (adjmatrix[i] & jbit)
         weight[j]++;
     for (int j = 0; j < m; j++)
-      if (weight[j] >= n_over_best)
+      if (weight[j] >= n_max_frags)
         goto takeout;
 
     iterate_recurse(i+1, adjmatrix[i]);
 
   takeout:
-    for (int j = 0; j < m; j++)
-      if (adjmatrix[i] & one_adj_bit(j))
+    FOR_BITS(j,m)
+      if (adjmatrix[i] & jbit)
         weight[j]--;
 
   again:
@@ -641,6 +687,14 @@ static void iterate(void) {
 
 static void report(void) {
   fprintf(stderr, "\n");
+  if (best_adjmatrix) {
+    int i;
+    fprintf(stderr,"  ");
+    for (i=0; i<n; i++) fprintf(stderr, " %"PRADJ, best_adjmatrix[i]);
+  }
+  fprintf(stderr, " best=%-12.8f nf<=%d mf<=%d\n",
+	  best, n_max_frags, m_max_frags);
+  printf("%d into %d: ", n, m);
   if (best_prob) {
     double min = glp_get_obj_val(best_prob);
     double a[n][m];
@@ -655,7 +709,7 @@ static void report(void) {
         continue;
       a[x][y] = min + glp_get_col_prim(best_prob, i);
     }
-    printf("%d into %d: min fragment %g   [%s]\n", n, m, min, VERSION);
+    printf("min fragment %g", min);
     for (i = 0; i < n; i++) {
       for (j = 0; j < m; j++) {
         if (a[i][j])
@@ -666,6 +720,7 @@ static void report(void) {
       printf("\n");
     }
   }
+  printf("   [%s]\n", VERSION);
   if (ferror(stdout) || fclose(stdout)) { perror("stdout"); exit(-1); }
 }
  
@@ -674,6 +729,7 @@ int main(int argc, char **argv) {
   while ((opt = getopt(argc,argv,"j:")) >= 0) {
     switch (opt) {
     case 'j': ncpus = atoi(optarg); break;
+    case 'b': set_best(atof(optarg)); break;
     case '+': assert(!"bad option");
     default: abort();
     }
@@ -683,6 +739,7 @@ int main(int argc, char **argv) {
   assert(argc==3);
   n = atoi(argv[1]);
   m = atoi(argv[2]);
+  assert(n > m);
 
   prep();