5 #include "heuristical.h"
6 #include "html_dumper.h"
10 #include "pbqp_edge_t.h"
11 #include "pbqp_node.h"
12 #include "pbqp_node_t.h"
15 static pbqp_edge **edge_bucket;
16 static pbqp_node **node_buckets[4];
17 static pbqp_node **reduced_bucket = NULL;
18 static int buckets_filled = 0;
20 static void insert_into_edge_bucket(pbqp_edge *edge)
22 unsigned bucket_len = ARR_LEN(edge_bucket);
24 if (edge->bucket_index < bucket_len && edge_bucket[edge->bucket_index]
26 /* Edge is already inserted. */
29 edge->bucket_index = bucket_len;
30 ARR_APP1(pbqp_edge *, edge_bucket, edge);
33 static void init_buckets(void)
37 edge_bucket = NEW_ARR_F(pbqp_edge *, 0);
38 reduced_bucket = NEW_ARR_F(pbqp_node *, 0);
40 for (i = 0; i < 4; ++i) {
41 node_buckets[i] = NEW_ARR_F(pbqp_node *, 0);
45 static void free_buckets(void)
49 for (i = 0; i < 4; ++i) {
50 DEL_ARR_F(node_buckets[i]);
51 node_buckets[i] = NULL;
54 DEL_ARR_F(edge_bucket);
57 DEL_ARR_F(reduced_bucket);
58 reduced_bucket = NULL;
63 static void fill_node_buckets(pbqp *pbqp)
69 node_len = pbqp->num_nodes;
71 for (node_index = 0; node_index < node_len; ++node_index) {
73 pbqp_node *node = get_node(pbqp, node_index);
77 arity = ARR_LEN(node->edges);
79 /* We have only one bucket for nodes with arity >= 3. */
84 node->bucket_index = ARR_LEN(node_buckets[arity]);
86 ARR_APP1(pbqp_node *, node_buckets[arity], node);
92 static void normalize_towards_source(pbqp *pbqp, pbqp_edge *edge)
106 src_node = edge->src;
107 tgt_node = edge->tgt;
111 src_vec = src_node->costs;
112 tgt_vec = tgt_node->costs;
116 src_len = src_vec->len;
117 tgt_len = tgt_vec->len;
124 /* Normalize towards source node. */
125 for (src_index = 0; src_index < src_len; ++src_index) {
126 num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
129 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
130 src_vec->entries[src_index].data = pbqp_add(
131 src_vec->entries[src_index].data, min);
133 if (min == INF_COSTS) {
134 insert_into_edge_bucket(edge);
140 static void normalize_towards_target(pbqp *pbqp, pbqp_edge *edge)
154 src_node = edge->src;
155 tgt_node = edge->tgt;
159 src_vec = src_node->costs;
160 tgt_vec = tgt_node->costs;
164 src_len = src_vec->len;
165 tgt_len = tgt_vec->len;
172 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
173 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
176 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
177 tgt_vec->entries[tgt_index].data = pbqp_add(
178 tgt_vec->entries[tgt_index].data, min);
180 if (min == INF_COSTS) {
181 insert_into_edge_bucket(edge);
187 static void reorder_node(pbqp_node *node)
191 unsigned old_bucket_len;
192 unsigned old_bucket_index;
193 pbqp_node **old_bucket;
196 if (!buckets_filled) return;
200 arity = ARR_LEN(node->edges);
202 /* Same bucket as before */
203 if (arity > 2) return;
205 /* Assume node lost one incident edge. */
206 old_arity = arity + 1;
207 old_bucket = node_buckets[old_arity];
208 old_bucket_len = ARR_LEN(old_bucket);
209 old_bucket_index = node->bucket_index;
211 if (old_bucket_len <= old_bucket_index || old_bucket[old_bucket_index]
213 unsigned bucket_len = ARR_LEN(node_buckets[arity]);
215 /* Old arity is new arity, so we have nothing to do. */
216 assert(old_bucket_index < bucket_len);
217 assert(node_buckets[arity][old_bucket_index] == node);
221 assert(old_bucket[old_bucket_index] == node);
223 /* Delete node from old bucket... */
224 other = old_bucket[old_bucket_len - 1];
225 other->bucket_index = old_bucket_index;
226 old_bucket[old_bucket_index] = other;
227 ARR_SHRINKLEN(node_buckets[old_arity], old_bucket_len - 1);
229 /* ..and add to new one. */
230 node->bucket_index = ARR_LEN(node_buckets[arity]);
231 ARR_APP1(pbqp_node*, node_buckets[arity], node);
234 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
247 src_node = edge->src;
248 tgt_node = edge->tgt;
252 /* If edge are already deleted, we have nothing to do. */
253 if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
256 if (pbqp->dump_file) {
258 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
259 dump_section(pbqp->dump_file, 3, txt);
262 src_vec = src_node->costs;
263 tgt_vec = tgt_node->costs;
267 src_len = src_vec->len;
268 tgt_len = tgt_vec->len;
275 if (pbqp->dump_file) {
276 fputs("Input:<br>\n", pbqp->dump_file);
277 dump_simplifyedge(pbqp, edge);
280 normalize_towards_source(pbqp, edge);
281 normalize_towards_target(pbqp, edge);
283 if (pbqp->dump_file) {
284 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
285 dump_simplifyedge(pbqp, edge);
288 if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
289 if (pbqp->dump_file) {
290 fputs("edge has been eliminated<br>\n", pbqp->dump_file);
294 reorder_node(src_node);
295 reorder_node(tgt_node);
299 void solve_pbqp_heuristical(pbqp *pbqp)
306 if (pbqp->dump_file) {
307 pbqp_dump_input(pbqp);
308 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
311 node_len = pbqp->num_nodes;
315 /* First simplify all edges. */
316 for (node_index = 0; node_index < node_len; ++node_index) {
318 pbqp_node *node = get_node(pbqp, node_index);
325 edge_len = ARR_LEN(edges);
327 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
328 pbqp_edge *edge = edges[edge_index];
330 /* Simplify only once per edge. */
331 if (node != edge->src) continue;
333 simplify_edge(pbqp, edge);
337 /* Put node into bucket representing their arity. */
338 fill_node_buckets(pbqp);
341 if (ARR_LEN(edge_bucket) > 0) {
343 } else if (ARR_LEN(node_buckets[1]) > 0) {
345 } else if (ARR_LEN(node_buckets[2]) > 0) {
347 } else if (ARR_LEN(node_buckets[3]) > 0) {
354 if (pbqp->dump_file) {
355 dump_section(pbqp->dump_file, 1, "4. Determine Solution/Minimum");
356 dump_section(pbqp->dump_file, 2, "4.1. Trivial Solution");
359 /* Solve trivial nodes and calculate solution. */
360 node_len = ARR_LEN(node_buckets[0]);
361 for (node_index = 0; node_index < node_len; ++node_index) {
362 pbqp_node *node = node_buckets[0][node_index];
365 node->solution = vector_get_min_index(node->costs);
366 pbqp->solution = pbqp_add(pbqp->solution,
367 node->costs->entries[node->solution].data);
368 if (pbqp->dump_file) {
369 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
370 dump_node(pbqp, node);
374 if (pbqp->dump_file) {
375 dump_section(pbqp->dump_file, 2, "Minimum");
376 fprintf(pbqp->dump_file, "Minimum is equal to %d.", pbqp->solution);
377 dump_section(pbqp->dump_file, 2, "Back Propagation");
380 /* Solve reduced nodes. */
381 node_len = ARR_LEN(reduced_bucket);
382 for (node_index = node_len; node_index > 0; --node_index) {
383 pbqp_node *node = reduced_bucket[node_index - 1];
386 switch (ARR_LEN(node->edges)) {
388 back_propagate_RI(pbqp, node);
391 back_propagate_RII(pbqp, node);
394 panic("Only nodes with degree one or two should be in this bucket");
402 void apply_edge(pbqp *pbqp)
404 unsigned bucket_len = ARR_LEN(edge_bucket);
405 pbqp_edge *edge = edge_bucket[bucket_len - 1];
407 ARR_SHRINKLEN(edge_bucket, (int)bucket_len - 1);
409 simplify_edge(pbqp, edge);
412 void apply_RI(pbqp *pbqp)
414 pbqp_node **bucket = node_buckets[1];
415 unsigned bucket_len = ARR_LEN(bucket);
416 pbqp_node *node = bucket[bucket_len - 1];
417 pbqp_edge *edge = node->edges[0];
418 pbqp_matrix *mat = edge->costs;
419 int is_src = edge->src == node;
420 pbqp_node *other_node;
423 other_node = edge->tgt;
425 other_node = edge->src;
428 if (pbqp->dump_file) {
430 sprintf(txt, "RI-Reduktion of Node n%d", node->index);
431 dump_section(pbqp->dump_file, 2, txt);
432 pbqp_dump_graph(pbqp);
433 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
434 dump_node(pbqp, node);
435 dump_node(pbqp, other_node);
436 dump_edge(pbqp, edge);
440 pbqp_matrix_add_to_all_cols(mat, node->costs);
441 normalize_towards_target(pbqp, edge);
443 pbqp_matrix_add_to_all_rows(mat, node->costs);
444 normalize_towards_source(pbqp, edge);
446 disconnect_edge(other_node, edge);
448 if (pbqp->dump_file) {
449 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
450 dump_node(pbqp, other_node);
453 /* Remove node from bucket... */
454 ARR_SHRINKLEN(bucket, (int)bucket_len - 1);
455 reorder_node(other_node);
457 /* ...and add it to back propagation list. */
458 node->bucket_index = ARR_LEN(reduced_bucket);
459 ARR_APP1(pbqp_node *, reduced_bucket, node);
462 void apply_RII(pbqp *pbqp)
464 pbqp_node **bucket = node_buckets[2];
465 unsigned bucket_len = ARR_LEN(bucket);
466 pbqp_node *node = bucket[bucket_len - 1];
467 pbqp_edge *src_edge = node->edges[0];
468 pbqp_edge *tgt_edge = node->edges[1];
469 int src_is_src = src_edge->src == node;
470 int tgt_is_src = tgt_edge->src == node;
471 pbqp_matrix *src_mat;
472 pbqp_matrix *tgt_mat;
489 src_node = src_edge->tgt;
491 src_node = src_edge->src;
495 tgt_node = tgt_edge->tgt;
497 tgt_node = tgt_edge->src;
500 /* Swap nodes if necessary. */
501 if (tgt_node->index < src_node->index) {
513 src_is_src = src_edge->src == node;
514 tgt_is_src = tgt_edge->src == node;
517 if (pbqp->dump_file) {
519 sprintf(txt, "RII-Reduktion of Node n%d", node->index);
520 dump_section(pbqp->dump_file, 2, txt);
521 pbqp_dump_graph(pbqp);
522 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
523 dump_node(pbqp, src_node);
524 dump_edge(pbqp, src_edge);
525 dump_node(pbqp, node);
526 dump_edge(pbqp, tgt_edge);
527 dump_node(pbqp, tgt_node);
530 src_mat = src_edge->costs;
531 tgt_mat = tgt_edge->costs;
533 src_vec = src_node->costs;
534 tgt_vec = tgt_node->costs;
535 node_vec = node->costs;
537 row_len = src_vec->len;
538 col_len = tgt_vec->len;
539 node_len = node_vec->len;
541 mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
543 for (row_index = 0; row_index < row_len; ++row_index) {
544 for (col_index = 0; col_index < col_len; ++col_index) {
545 vec = vector_copy(pbqp, node_vec);
548 vector_add_matrix_col(vec, src_mat, row_index);
550 vector_add_matrix_row(vec, src_mat, row_index);
554 vector_add_matrix_col(vec, tgt_mat, col_index);
556 vector_add_matrix_row(vec, tgt_mat, col_index);
559 mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
561 obstack_free(&pbqp->obstack, vec);
565 pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
567 /* Disconnect node. */
568 disconnect_edge(src_node, src_edge);
569 disconnect_edge(tgt_node, tgt_edge);
571 /* Remove node from bucket... */
572 ARR_SHRINKLEN(bucket, (int)bucket_len - 1);
574 /* ...and add it to back propagation list. */
575 node->bucket_index = ARR_LEN(reduced_bucket);
576 ARR_APP1(pbqp_node *, reduced_bucket, node);
579 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
581 pbqp_matrix_add(edge->costs, mat);
583 /* Free local matrix. */
584 obstack_free(&pbqp->obstack, mat);
586 reorder_node(src_node);
587 reorder_node(tgt_node);
590 if (pbqp->dump_file) {
591 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
592 dump_edge(pbqp, edge);
595 /* Edge has changed so we simplify it. */
596 simplify_edge(pbqp, edge);
599 void apply_RN(pbqp *pbqp)
601 pbqp_node **bucket = node_buckets[3];
602 unsigned bucket_len = ARR_LEN(bucket);
603 pbqp_node *node = bucket[bucket_len - 1];
605 vector *node_vec = node->costs;
609 unsigned edge_len = ARR_LEN(node->edges);
611 unsigned node_len = node_vec->len;
612 unsigned min_index = 0;
618 for (node_index = 0; node_index < node_len; ++node_index) {
621 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
622 edge = node->edges[edge_index];
624 is_src = edge->src == node;
627 vec = vector_copy(pbqp, edge->tgt->costs);
628 vector_add_matrix_row(vec, mat, node_index);
630 vec = vector_copy(pbqp, edge->src->costs);
631 vector_add_matrix_col(vec, mat, node_index);
634 value = pbqp_add(value, vector_get_min(vec));
636 obstack_free(&pbqp->obstack, vec);
641 min_index = node_index;
645 node->solution = min_index;
647 /* Now that we found the local minimum set all other costs to infinity. */
648 for (node_index = 0; node_index < node_len; ++node_index) {
649 if (node_index != min_index) {
650 node_vec->entries[node_index].data = INF_COSTS;
654 /* Add all incident edges to edge bucket, since they are now independent. */
655 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
656 insert_into_edge_bucket(node->edges[edge_index]);
660 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
671 edge = node->edges[0];
673 is_src = edge->src == node;
679 vector_add_matrix_col(vec, mat, other->solution);
683 vector_add_matrix_row(vec, mat, other->solution);
686 node->solution = vector_get_min_index(vec);
687 if (pbqp->dump_file) {
688 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
692 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
694 pbqp_edge *src_edge = node->edges[0];
695 pbqp_edge *tgt_edge = node->edges[1];
696 int src_is_src = src_edge->src == node;
697 int tgt_is_src = tgt_edge->src == node;
698 pbqp_matrix *src_mat;
699 pbqp_matrix *tgt_mat;
710 src_node = src_edge->tgt;
712 src_node = src_edge->src;
716 tgt_node = tgt_edge->tgt;
718 tgt_node = tgt_edge->src;
721 /* Swap nodes if necessary. */
722 if (tgt_node->index < src_node->index) {
734 src_is_src = src_edge->src == node;
735 tgt_is_src = tgt_edge->src == node;
738 src_mat = src_edge->costs;
739 tgt_mat = tgt_edge->costs;
741 node_vec = node->costs;
743 row_index = src_node->solution;
744 col_index = tgt_node->solution;
746 vec = vector_copy(pbqp, node_vec);
749 vector_add_matrix_col(vec, src_mat, row_index);
751 vector_add_matrix_row(vec, src_mat, row_index);
755 vector_add_matrix_col(vec, tgt_mat, col_index);
757 vector_add_matrix_row(vec, tgt_mat, col_index);
760 node->solution = vector_get_min_index(vec);
761 if (pbqp->dump_file) {
762 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
765 obstack_free(&pbqp->obstack, vec);
768 int node_is_reduced(pbqp_node *node)
770 if (!reduced_bucket) return 0;
773 if (ARR_LEN(node->edges) == 0) return 1;
775 unsigned bucket_length = ARR_LEN(reduced_bucket);
776 unsigned bucket_index = node->bucket_index;
778 return bucket_index < bucket_length && reduced_bucket[bucket_index] == node;