*
* 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
*/
/*
*
* 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
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;
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 -----*/
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 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) {
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
glp_set_obj_coef(prob, X_minimum, 1);
for (i=0; i<n; i++) {
- for (j=0, jbit=1; j<m; j++, jbit<<=1) {
+ FOR_BITS(j,m) {
if (!(adjmatrix[i] & jbit))
continue;
/* x_total_i += x_minimum */
AdjWord jbit;
if (i >= n) {
+ for (j=0; j<m; j++)
+ if (weight[j] < 2)
+ return;
+
printcounter++;
optimise(!(printcounter & 0xfff));
return;
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]);
assert(argc==3);
n = atoi(argv[1]);
m = atoi(argv[2]);
+ assert(n > m);
prep();