6 #include "heuristical.h"
7 #include "html_dumper.h"
10 #include "pbqp_edge.h"
11 #include "pbqp_edge_t.h"
12 #include "pbqp_node.h"
13 #include "pbqp_node_t.h"
16 static pbqp_edge **edge_bucket;
17 static pbqp_node **node_buckets[4];
18 static pbqp_node **reduced_bucket = NULL;
19 static int buckets_filled = 0;
21 static void insert_into_edge_bucket(pbqp_edge *edge)
23 unsigned bucket_len = ARR_LEN(edge_bucket);
25 if (edge->bucket_index < bucket_len && edge_bucket[edge->bucket_index]
27 /* Edge is already inserted. */
30 edge->bucket_index = bucket_len;
31 ARR_APP1(pbqp_edge *, edge_bucket, edge);
34 static void init_buckets(void)
38 edge_bucket = NEW_ARR_F(pbqp_edge *, 0);
39 reduced_bucket = NEW_ARR_F(pbqp_node *, 0);
41 for (i = 0; i < 4; ++i) {
42 node_buckets[i] = NEW_ARR_F(pbqp_node *, 0);
46 static void free_buckets(void)
50 for (i = 0; i < 4; ++i) {
51 DEL_ARR_F(node_buckets[i]);
52 node_buckets[i] = NULL;
55 DEL_ARR_F(edge_bucket);
58 DEL_ARR_F(reduced_bucket);
59 reduced_bucket = NULL;
64 static void fill_node_buckets(pbqp *pbqp)
70 node_len = pbqp->num_nodes;
72 for (node_index = 0; node_index < node_len; ++node_index) {
74 pbqp_node *node = get_node(pbqp, node_index);
78 arity = ARR_LEN(node->edges);
80 /* We have only one bucket for nodes with arity >= 3. */
85 node->bucket_index = node_bucket_get_length(node_buckets[arity]);
87 ARR_APP1(pbqp_node *, node_buckets[arity], node);
93 static void normalize_towards_source(pbqp *pbqp, pbqp_edge *edge)
107 src_node = edge->src;
108 tgt_node = edge->tgt;
112 src_vec = src_node->costs;
113 tgt_vec = tgt_node->costs;
117 src_len = src_vec->len;
118 tgt_len = tgt_vec->len;
125 /* Normalize towards source node. */
126 for (src_index = 0; src_index < src_len; ++src_index) {
127 num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
130 if (src_vec->entries[src_index].data == INF_COSTS) {
131 pbqp_matrix_set_row_value(mat, src_index, 0);
133 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
135 src_vec->entries[src_index].data = pbqp_add(
136 src_vec->entries[src_index].data, min);
138 if (min == INF_COSTS) {
140 unsigned edge_len = ARR_LEN(src_node->edges);
142 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
143 pbqp_edge *edge_candidate = src_node->edges[edge_index];
144 if (edge_candidate != edge) {
145 insert_into_edge_bucket(edge_candidate);
153 static void normalize_towards_target(pbqp *pbqp, pbqp_edge *edge)
167 src_node = edge->src;
168 tgt_node = edge->tgt;
172 src_vec = src_node->costs;
173 tgt_vec = tgt_node->costs;
177 src_len = src_vec->len;
178 tgt_len = tgt_vec->len;
185 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
186 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
189 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
190 pbqp_matrix_set_col_value(mat, tgt_index, 0);
192 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
194 tgt_vec->entries[tgt_index].data = pbqp_add(
195 tgt_vec->entries[tgt_index].data, min);
197 if (min == INF_COSTS) {
199 unsigned edge_len = ARR_LEN(tgt_node->edges);
201 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
202 pbqp_edge *edge_candidate = tgt_node->edges[edge_index];
203 if (edge_candidate != edge) {
204 insert_into_edge_bucket(edge_candidate);
212 static void reorder_node(pbqp_node *node)
216 unsigned old_bucket_len;
217 unsigned old_bucket_index;
218 pbqp_node **old_bucket;
221 if (!buckets_filled) return;
225 arity = ARR_LEN(node->edges);
227 /* Same bucket as before */
228 if (arity > 2) return;
230 /* Assume node lost one incident edge. */
231 old_arity = arity + 1;
232 old_bucket = node_buckets[old_arity];
233 old_bucket_len = node_bucket_get_length(old_bucket);
234 old_bucket_index = node->bucket_index;
236 if (old_bucket_len <= old_bucket_index || old_bucket[old_bucket_index]
238 unsigned bucket_len = node_bucket_get_length(node_buckets[arity]);
240 /* Old arity is new arity, so we have nothing to do. */
241 assert(old_bucket_index < bucket_len);
242 assert(node_buckets[arity][old_bucket_index] == node);
246 assert(old_bucket[old_bucket_index] == node);
248 /* Delete node from old bucket... */
249 other = old_bucket[old_bucket_len - 1];
250 other->bucket_index = old_bucket_index;
251 old_bucket[old_bucket_index] = other;
252 ARR_SHRINKLEN(node_buckets[old_arity], old_bucket_len - 1);
254 /* ..and add to new one. */
255 node->bucket_index = node_bucket_get_length(node_buckets[arity]);
256 ARR_APP1(pbqp_node*, node_buckets[arity], node);
259 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
272 src_node = edge->src;
273 tgt_node = edge->tgt;
277 /* If edge are already deleted, we have nothing to do. */
278 if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
281 if (pbqp->dump_file) {
283 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
284 dump_section(pbqp->dump_file, 3, txt);
287 src_vec = src_node->costs;
288 tgt_vec = tgt_node->costs;
292 src_len = src_vec->len;
293 tgt_len = tgt_vec->len;
300 if (pbqp->dump_file) {
301 fputs("Input:<br>\n", pbqp->dump_file);
302 dump_simplifyedge(pbqp, edge);
305 normalize_towards_source(pbqp, edge);
306 normalize_towards_target(pbqp, edge);
308 if (pbqp->dump_file) {
309 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
310 dump_simplifyedge(pbqp, edge);
313 if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
314 if (pbqp->dump_file) {
315 fputs("edge has been eliminated<br>\n", pbqp->dump_file);
319 reorder_node(src_node);
320 reorder_node(tgt_node);
324 void solve_pbqp_heuristical(pbqp *pbqp)
331 if (pbqp->dump_file) {
332 pbqp_dump_input(pbqp);
333 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
336 node_len = pbqp->num_nodes;
340 /* First simplify all edges. */
341 for (node_index = 0; node_index < node_len; ++node_index) {
343 pbqp_node *node = get_node(pbqp, node_index);
350 edge_len = ARR_LEN(edges);
352 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
353 pbqp_edge *edge = edges[edge_index];
355 /* Simplify only once per edge. */
356 if (node != edge->src) continue;
358 simplify_edge(pbqp, edge);
362 /* Put node into bucket representing their arity. */
363 fill_node_buckets(pbqp);
366 if (ARR_LEN(edge_bucket) > 0) {
368 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
370 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
372 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
379 if (pbqp->dump_file) {
380 dump_section(pbqp->dump_file, 1, "4. Determine Solution/Minimum");
381 dump_section(pbqp->dump_file, 2, "4.1. Trivial Solution");
384 /* Solve trivial nodes and calculate solution. */
385 node_len = node_bucket_get_length(node_buckets[0]);
386 for (node_index = 0; node_index < node_len; ++node_index) {
387 pbqp_node *node = node_buckets[0][node_index];
390 node->solution = vector_get_min_index(node->costs);
391 pbqp->solution = pbqp_add(pbqp->solution,
392 node->costs->entries[node->solution].data);
393 if (pbqp->dump_file) {
394 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
395 dump_node(pbqp, node);
399 if (pbqp->dump_file) {
400 dump_section(pbqp->dump_file, 2, "Minimum");
401 fprintf(pbqp->dump_file, "Minimum is equal to %lld.", pbqp->solution);
402 dump_section(pbqp->dump_file, 2, "Back Propagation");
405 /* Solve reduced nodes. */
406 node_len = node_bucket_get_length(reduced_bucket);
407 for (node_index = node_len; node_index > 0; --node_index) {
408 pbqp_node *node = reduced_bucket[node_index - 1];
411 switch (ARR_LEN(node->edges)) {
413 back_propagate_RI(pbqp, node);
416 back_propagate_RII(pbqp, node);
419 panic("Only nodes with degree one or two should be in this bucket");
427 void apply_edge(pbqp *pbqp)
429 unsigned bucket_len = ARR_LEN(edge_bucket);
430 pbqp_edge *edge = edge_bucket[bucket_len - 1];
432 ARR_SHRINKLEN(edge_bucket, (int)bucket_len - 1);
434 simplify_edge(pbqp, edge);
437 void apply_RI(pbqp *pbqp)
439 pbqp_node **bucket = node_buckets[1];
440 unsigned bucket_len = node_bucket_get_length(bucket);
441 pbqp_node *node = bucket[bucket_len - 1];
442 pbqp_edge *edge = node->edges[0];
443 pbqp_matrix *mat = edge->costs;
444 int is_src = edge->src == node;
445 pbqp_node *other_node;
448 other_node = edge->tgt;
450 other_node = edge->src;
453 if (pbqp->dump_file) {
455 sprintf(txt, "RI-Reduction of Node n%d", node->index);
456 dump_section(pbqp->dump_file, 2, txt);
457 pbqp_dump_graph(pbqp);
458 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
459 dump_node(pbqp, node);
460 dump_node(pbqp, other_node);
461 dump_edge(pbqp, edge);
465 pbqp_matrix_add_to_all_cols(mat, node->costs);
466 normalize_towards_target(pbqp, edge);
468 pbqp_matrix_add_to_all_rows(mat, node->costs);
469 normalize_towards_source(pbqp, edge);
471 disconnect_edge(other_node, edge);
473 if (pbqp->dump_file) {
474 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
475 dump_node(pbqp, other_node);
478 /* Remove node from bucket... */
479 ARR_SHRINKLEN(bucket, (int)bucket_len - 1);
480 reorder_node(other_node);
482 /* ...and add it to back propagation list. */
483 node->bucket_index = node_bucket_get_length(reduced_bucket);
484 ARR_APP1(pbqp_node *, reduced_bucket, node);
487 void apply_RII(pbqp *pbqp)
489 pbqp_node **bucket = node_buckets[2];
490 unsigned bucket_len = node_bucket_get_length(bucket);
491 pbqp_node *node = bucket[bucket_len - 1];
492 pbqp_edge *src_edge = node->edges[0];
493 pbqp_edge *tgt_edge = node->edges[1];
494 int src_is_src = src_edge->src == node;
495 int tgt_is_src = tgt_edge->src == node;
496 pbqp_matrix *src_mat;
497 pbqp_matrix *tgt_mat;
514 src_node = src_edge->tgt;
516 src_node = src_edge->src;
520 tgt_node = tgt_edge->tgt;
522 tgt_node = tgt_edge->src;
525 /* Swap nodes if necessary. */
526 if (tgt_node->index < src_node->index) {
538 src_is_src = src_edge->src == node;
539 tgt_is_src = tgt_edge->src == node;
542 if (pbqp->dump_file) {
544 sprintf(txt, "RII-Reduction of Node n%d", node->index);
545 dump_section(pbqp->dump_file, 2, txt);
546 pbqp_dump_graph(pbqp);
547 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
548 dump_node(pbqp, src_node);
549 dump_edge(pbqp, src_edge);
550 dump_node(pbqp, node);
551 dump_edge(pbqp, tgt_edge);
552 dump_node(pbqp, tgt_node);
555 src_mat = src_edge->costs;
556 tgt_mat = tgt_edge->costs;
558 src_vec = src_node->costs;
559 tgt_vec = tgt_node->costs;
560 node_vec = node->costs;
562 row_len = src_vec->len;
563 col_len = tgt_vec->len;
564 node_len = node_vec->len;
566 mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
568 for (row_index = 0; row_index < row_len; ++row_index) {
569 for (col_index = 0; col_index < col_len; ++col_index) {
570 vec = vector_copy(pbqp, node_vec);
573 vector_add_matrix_col(vec, src_mat, row_index);
575 vector_add_matrix_row(vec, src_mat, row_index);
579 vector_add_matrix_col(vec, tgt_mat, col_index);
581 vector_add_matrix_row(vec, tgt_mat, col_index);
584 mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
586 obstack_free(&pbqp->obstack, vec);
590 pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
592 /* Disconnect node. */
593 disconnect_edge(src_node, src_edge);
594 disconnect_edge(tgt_node, tgt_edge);
596 /* Remove node from bucket... */
597 ARR_SHRINKLEN(bucket, (int)bucket_len - 1);
599 /* ...and add it to back propagation list. */
600 node->bucket_index = node_bucket_get_length(reduced_bucket);
601 ARR_APP1(pbqp_node *, reduced_bucket, node);
604 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
606 pbqp_matrix_add(edge->costs, mat);
608 /* Free local matrix. */
609 obstack_free(&pbqp->obstack, mat);
611 reorder_node(src_node);
612 reorder_node(tgt_node);
615 if (pbqp->dump_file) {
616 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
617 dump_edge(pbqp, edge);
620 /* Edge has changed so we simplify it. */
621 simplify_edge(pbqp, edge);
624 void apply_RN(pbqp *pbqp)
626 pbqp_node **bucket = node_buckets[3];
627 unsigned bucket_len = node_bucket_get_length(bucket);
628 unsigned bucket_index;
629 pbqp_node *node = NULL;
635 unsigned max_degree = 0;
638 unsigned min_index = 0;
644 /* Search for node with maximum degree. */
645 for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
646 pbqp_node *candidate = bucket[bucket_index];
647 unsigned degree = ARR_LEN(candidate->edges);
649 if (degree > max_degree) {
655 node_vec = node->costs;
656 node_len = node_vec->len;
658 if (pbqp->dump_file) {
660 sprintf(txt, "RN-Reduction of Node n%d", node->index);
661 dump_section(pbqp->dump_file, 2, txt);
662 pbqp_dump_graph(pbqp);
665 for (node_index = 0; node_index < node_len; ++node_index) {
666 num value = node_vec->entries[node_index].data;
668 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
669 edge = node->edges[edge_index];
671 is_src = edge->src == node;
674 vec = vector_copy(pbqp, edge->tgt->costs);
675 vector_add_matrix_row(vec, mat, node_index);
677 vec = vector_copy(pbqp, edge->src->costs);
678 vector_add_matrix_col(vec, mat, node_index);
681 value = pbqp_add(value, vector_get_min(vec));
683 obstack_free(&pbqp->obstack, vec);
688 min_index = node_index;
692 if (pbqp->dump_file) {
693 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
694 node->index, min_index);
695 fprintf(pbqp->dump_file, "Minimal cost of RN reduction: %lld<br>\n",
699 node->solution = min_index;
701 /* Now that we found the local minimum set all other costs to infinity. */
702 for (node_index = 0; node_index < node_len; ++node_index) {
703 if (node_index != min_index) {
704 node_vec->entries[node_index].data = INF_COSTS;
708 /* Add all incident edges to edge bucket, since they are now independent. */
709 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
710 insert_into_edge_bucket(node->edges[edge_index]);
714 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
725 edge = node->edges[0];
727 is_src = edge->src == node;
733 vector_add_matrix_col(vec, mat, other->solution);
737 vector_add_matrix_row(vec, mat, other->solution);
740 node->solution = vector_get_min_index(vec);
741 if (pbqp->dump_file) {
742 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
746 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
748 pbqp_edge *src_edge = node->edges[0];
749 pbqp_edge *tgt_edge = node->edges[1];
750 int src_is_src = src_edge->src == node;
751 int tgt_is_src = tgt_edge->src == node;
752 pbqp_matrix *src_mat;
753 pbqp_matrix *tgt_mat;
764 src_node = src_edge->tgt;
766 src_node = src_edge->src;
770 tgt_node = tgt_edge->tgt;
772 tgt_node = tgt_edge->src;
775 /* Swap nodes if necessary. */
776 if (tgt_node->index < src_node->index) {
788 src_is_src = src_edge->src == node;
789 tgt_is_src = tgt_edge->src == node;
792 src_mat = src_edge->costs;
793 tgt_mat = tgt_edge->costs;
795 node_vec = node->costs;
797 row_index = src_node->solution;
798 col_index = tgt_node->solution;
800 vec = vector_copy(pbqp, node_vec);
803 vector_add_matrix_col(vec, src_mat, row_index);
805 vector_add_matrix_row(vec, src_mat, row_index);
809 vector_add_matrix_col(vec, tgt_mat, col_index);
811 vector_add_matrix_row(vec, tgt_mat, col_index);
814 node->solution = vector_get_min_index(vec);
815 if (pbqp->dump_file) {
816 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
819 obstack_free(&pbqp->obstack, vec);
822 int node_is_reduced(pbqp_node *node)
824 if (!reduced_bucket) return 0;
827 if (ARR_LEN(node->edges) == 0) return 1;
829 unsigned bucket_length = node_bucket_get_length(reduced_bucket);
830 unsigned bucket_index = node->bucket_index;
832 return bucket_index < bucket_length && reduced_bucket[bucket_index] == node;