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 = edge_bucket_get_length(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_init(&edge_bucket);
39 node_bucket_init(&reduced_bucket);
41 for (i = 0; i < 4; ++i) {
42 node_bucket_init(&node_buckets[i]);
46 static void free_buckets(void)
50 for (i = 0; i < 4; ++i) {
51 node_bucket_free(&node_buckets[i]);
54 edge_bucket_free(&edge_bucket);
55 node_bucket_free(&reduced_bucket);
60 static void fill_node_buckets(pbqp *pbqp)
66 node_len = pbqp->num_nodes;
68 for (node_index = 0; node_index < node_len; ++node_index) {
70 pbqp_node *node = get_node(pbqp, node_index);
74 arity = ARR_LEN(node->edges);
76 /* We have only one bucket for nodes with arity >= 3. */
81 node_bucket_insert(&node_buckets[arity], node);
87 static void normalize_towards_source(pbqp *pbqp, pbqp_edge *edge)
101 src_node = edge->src;
102 tgt_node = edge->tgt;
106 src_vec = src_node->costs;
107 tgt_vec = tgt_node->costs;
111 src_len = src_vec->len;
112 tgt_len = tgt_vec->len;
119 /* Normalize towards source node. */
120 for (src_index = 0; src_index < src_len; ++src_index) {
121 num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
124 if (src_vec->entries[src_index].data == INF_COSTS) {
125 pbqp_matrix_set_row_value(mat, src_index, 0);
127 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
129 src_vec->entries[src_index].data = pbqp_add(
130 src_vec->entries[src_index].data, min);
132 if (min == INF_COSTS) {
134 unsigned edge_len = ARR_LEN(src_node->edges);
136 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
137 pbqp_edge *edge_candidate = src_node->edges[edge_index];
138 if (edge_candidate != edge) {
139 insert_into_edge_bucket(edge_candidate);
147 static void normalize_towards_target(pbqp *pbqp, pbqp_edge *edge)
161 src_node = edge->src;
162 tgt_node = edge->tgt;
166 src_vec = src_node->costs;
167 tgt_vec = tgt_node->costs;
171 src_len = src_vec->len;
172 tgt_len = tgt_vec->len;
179 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
180 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
183 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
184 pbqp_matrix_set_col_value(mat, tgt_index, 0);
186 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
188 tgt_vec->entries[tgt_index].data = pbqp_add(
189 tgt_vec->entries[tgt_index].data, min);
191 if (min == INF_COSTS) {
193 unsigned edge_len = ARR_LEN(tgt_node->edges);
195 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
196 pbqp_edge *edge_candidate = tgt_node->edges[edge_index];
197 if (edge_candidate != edge) {
198 insert_into_edge_bucket(edge_candidate);
206 static void reorder_node(pbqp_node *node)
210 unsigned old_bucket_len;
211 unsigned old_bucket_index;
212 pbqp_node **old_bucket;
215 if (!buckets_filled) return;
219 arity = ARR_LEN(node->edges);
221 /* Same bucket as before */
222 if (arity > 2) return;
224 /* Assume node lost one incident edge. */
225 old_arity = arity + 1;
226 old_bucket = node_buckets[old_arity];
227 old_bucket_len = node_bucket_get_length(old_bucket);
228 old_bucket_index = node->bucket_index;
230 if (old_bucket_len <= old_bucket_index || old_bucket[old_bucket_index]
232 unsigned bucket_len = node_bucket_get_length(node_buckets[arity]);
234 /* Old arity is new arity, so we have nothing to do. */
235 assert(old_bucket_index < bucket_len);
236 assert(node_buckets[arity][old_bucket_index] == node);
240 assert(old_bucket[old_bucket_index] == node);
242 /* Delete node from old bucket... */
243 other = old_bucket[old_bucket_len - 1];
244 other->bucket_index = old_bucket_index;
245 old_bucket[old_bucket_index] = other;
246 ARR_SHRINKLEN(node_buckets[old_arity], old_bucket_len - 1);
248 /* ..and add to new one. */
249 node->bucket_index = node_bucket_get_length(node_buckets[arity]);
250 ARR_APP1(pbqp_node*, node_buckets[arity], node);
253 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
266 src_node = edge->src;
267 tgt_node = edge->tgt;
271 /* If edge are already deleted, we have nothing to do. */
272 if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
275 if (pbqp->dump_file) {
277 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
278 dump_section(pbqp->dump_file, 3, txt);
281 src_vec = src_node->costs;
282 tgt_vec = tgt_node->costs;
286 src_len = src_vec->len;
287 tgt_len = tgt_vec->len;
294 if (pbqp->dump_file) {
295 fputs("Input:<br>\n", pbqp->dump_file);
296 dump_simplifyedge(pbqp, edge);
299 normalize_towards_source(pbqp, edge);
300 normalize_towards_target(pbqp, edge);
302 if (pbqp->dump_file) {
303 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
304 dump_simplifyedge(pbqp, edge);
307 if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
308 if (pbqp->dump_file) {
309 fputs("edge has been eliminated<br>\n", pbqp->dump_file);
313 reorder_node(src_node);
314 reorder_node(tgt_node);
318 void solve_pbqp_heuristical(pbqp *pbqp)
325 if (pbqp->dump_file) {
326 pbqp_dump_input(pbqp);
327 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
330 node_len = pbqp->num_nodes;
334 /* First simplify all edges. */
335 for (node_index = 0; node_index < node_len; ++node_index) {
337 pbqp_node *node = get_node(pbqp, node_index);
344 edge_len = ARR_LEN(edges);
346 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
347 pbqp_edge *edge = edges[edge_index];
349 /* Simplify only once per edge. */
350 if (node != edge->src) continue;
352 simplify_edge(pbqp, edge);
356 /* Put node into bucket representing their arity. */
357 fill_node_buckets(pbqp);
360 if (edge_bucket_get_length(edge_bucket) > 0) {
362 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
364 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
366 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
373 if (pbqp->dump_file) {
374 dump_section(pbqp->dump_file, 1, "4. Determine Solution/Minimum");
375 dump_section(pbqp->dump_file, 2, "4.1. Trivial Solution");
378 /* Solve trivial nodes and calculate solution. */
379 node_len = node_bucket_get_length(node_buckets[0]);
380 for (node_index = 0; node_index < node_len; ++node_index) {
381 pbqp_node *node = node_buckets[0][node_index];
384 node->solution = vector_get_min_index(node->costs);
385 pbqp->solution = pbqp_add(pbqp->solution,
386 node->costs->entries[node->solution].data);
387 if (pbqp->dump_file) {
388 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
389 dump_node(pbqp, node);
393 if (pbqp->dump_file) {
394 dump_section(pbqp->dump_file, 2, "Minimum");
395 fprintf(pbqp->dump_file, "Minimum is equal to %lld.", pbqp->solution);
396 dump_section(pbqp->dump_file, 2, "Back Propagation");
399 /* Solve reduced nodes. */
400 node_len = node_bucket_get_length(reduced_bucket);
401 for (node_index = node_len; node_index > 0; --node_index) {
402 pbqp_node *node = reduced_bucket[node_index - 1];
405 switch (ARR_LEN(node->edges)) {
407 back_propagate_RI(pbqp, node);
410 back_propagate_RII(pbqp, node);
413 panic("Only nodes with degree one or two should be in this bucket");
421 void apply_edge(pbqp *pbqp)
423 pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
425 simplify_edge(pbqp, edge);
428 void apply_RI(pbqp *pbqp)
430 pbqp_node *node = node_bucket_pop(&node_buckets[1]);
431 pbqp_edge *edge = node->edges[0];
432 pbqp_matrix *mat = edge->costs;
433 int is_src = edge->src == node;
434 pbqp_node *other_node;
437 other_node = edge->tgt;
439 other_node = edge->src;
442 if (pbqp->dump_file) {
444 sprintf(txt, "RI-Reduction of Node n%d", node->index);
445 dump_section(pbqp->dump_file, 2, txt);
446 pbqp_dump_graph(pbqp);
447 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
448 dump_node(pbqp, node);
449 dump_node(pbqp, other_node);
450 dump_edge(pbqp, edge);
454 pbqp_matrix_add_to_all_cols(mat, node->costs);
455 normalize_towards_target(pbqp, edge);
457 pbqp_matrix_add_to_all_rows(mat, node->costs);
458 normalize_towards_source(pbqp, edge);
460 disconnect_edge(other_node, edge);
462 if (pbqp->dump_file) {
463 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
464 dump_node(pbqp, other_node);
467 reorder_node(other_node);
469 /* Add node to back propagation list. */
470 node_bucket_insert(&reduced_bucket, node);
473 void apply_RII(pbqp *pbqp)
475 pbqp_node *node = node_bucket_pop(&node_buckets[2]);
476 pbqp_edge *src_edge = node->edges[0];
477 pbqp_edge *tgt_edge = node->edges[1];
478 int src_is_src = src_edge->src == node;
479 int tgt_is_src = tgt_edge->src == node;
480 pbqp_matrix *src_mat;
481 pbqp_matrix *tgt_mat;
498 src_node = src_edge->tgt;
500 src_node = src_edge->src;
504 tgt_node = tgt_edge->tgt;
506 tgt_node = tgt_edge->src;
509 /* Swap nodes if necessary. */
510 if (tgt_node->index < src_node->index) {
522 src_is_src = src_edge->src == node;
523 tgt_is_src = tgt_edge->src == node;
526 if (pbqp->dump_file) {
528 sprintf(txt, "RII-Reduction of Node n%d", node->index);
529 dump_section(pbqp->dump_file, 2, txt);
530 pbqp_dump_graph(pbqp);
531 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
532 dump_node(pbqp, src_node);
533 dump_edge(pbqp, src_edge);
534 dump_node(pbqp, node);
535 dump_edge(pbqp, tgt_edge);
536 dump_node(pbqp, tgt_node);
539 src_mat = src_edge->costs;
540 tgt_mat = tgt_edge->costs;
542 src_vec = src_node->costs;
543 tgt_vec = tgt_node->costs;
544 node_vec = node->costs;
546 row_len = src_vec->len;
547 col_len = tgt_vec->len;
548 node_len = node_vec->len;
550 mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
552 for (row_index = 0; row_index < row_len; ++row_index) {
553 for (col_index = 0; col_index < col_len; ++col_index) {
554 vec = vector_copy(pbqp, node_vec);
557 vector_add_matrix_col(vec, src_mat, row_index);
559 vector_add_matrix_row(vec, src_mat, row_index);
563 vector_add_matrix_col(vec, tgt_mat, col_index);
565 vector_add_matrix_row(vec, tgt_mat, col_index);
568 mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
570 obstack_free(&pbqp->obstack, vec);
574 pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
576 /* Disconnect node. */
577 disconnect_edge(src_node, src_edge);
578 disconnect_edge(tgt_node, tgt_edge);
580 /* Add node to back propagation list. */
581 node_bucket_insert(&reduced_bucket, node);
584 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
586 pbqp_matrix_add(edge->costs, mat);
588 /* Free local matrix. */
589 obstack_free(&pbqp->obstack, mat);
591 reorder_node(src_node);
592 reorder_node(tgt_node);
595 if (pbqp->dump_file) {
596 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
597 dump_edge(pbqp, edge);
600 /* Edge has changed so we simplify it. */
601 simplify_edge(pbqp, edge);
604 void apply_RN(pbqp *pbqp)
606 pbqp_node **bucket = node_buckets[3];
607 unsigned bucket_len = node_bucket_get_length(bucket);
608 unsigned bucket_index;
609 pbqp_node *node = NULL;
615 unsigned max_degree = 0;
618 unsigned min_index = 0;
624 /* Search for node with maximum degree. */
625 for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
626 pbqp_node *candidate = bucket[bucket_index];
627 unsigned degree = ARR_LEN(candidate->edges);
629 if (degree > max_degree) {
635 node_vec = node->costs;
636 node_len = node_vec->len;
638 if (pbqp->dump_file) {
640 sprintf(txt, "RN-Reduction of Node n%d", node->index);
641 dump_section(pbqp->dump_file, 2, txt);
642 pbqp_dump_graph(pbqp);
645 for (node_index = 0; node_index < node_len; ++node_index) {
646 num value = node_vec->entries[node_index].data;
648 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
649 edge = node->edges[edge_index];
651 is_src = edge->src == node;
654 vec = vector_copy(pbqp, edge->tgt->costs);
655 vector_add_matrix_row(vec, mat, node_index);
657 vec = vector_copy(pbqp, edge->src->costs);
658 vector_add_matrix_col(vec, mat, node_index);
661 value = pbqp_add(value, vector_get_min(vec));
663 obstack_free(&pbqp->obstack, vec);
668 min_index = node_index;
672 if (pbqp->dump_file) {
673 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
674 node->index, min_index);
675 fprintf(pbqp->dump_file, "Minimal cost of RN reduction: %lld<br>\n",
679 node->solution = min_index;
681 /* Now that we found the local minimum set all other costs to infinity. */
682 for (node_index = 0; node_index < node_len; ++node_index) {
683 if (node_index != min_index) {
684 node_vec->entries[node_index].data = INF_COSTS;
688 /* Add all incident edges to edge bucket, since they are now independent. */
689 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
690 insert_into_edge_bucket(node->edges[edge_index]);
694 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
705 edge = node->edges[0];
707 is_src = edge->src == node;
713 vector_add_matrix_col(vec, mat, other->solution);
717 vector_add_matrix_row(vec, mat, other->solution);
720 node->solution = vector_get_min_index(vec);
721 if (pbqp->dump_file) {
722 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
726 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
728 pbqp_edge *src_edge = node->edges[0];
729 pbqp_edge *tgt_edge = node->edges[1];
730 int src_is_src = src_edge->src == node;
731 int tgt_is_src = tgt_edge->src == node;
732 pbqp_matrix *src_mat;
733 pbqp_matrix *tgt_mat;
744 src_node = src_edge->tgt;
746 src_node = src_edge->src;
750 tgt_node = tgt_edge->tgt;
752 tgt_node = tgt_edge->src;
755 /* Swap nodes if necessary. */
756 if (tgt_node->index < src_node->index) {
768 src_is_src = src_edge->src == node;
769 tgt_is_src = tgt_edge->src == node;
772 src_mat = src_edge->costs;
773 tgt_mat = tgt_edge->costs;
775 node_vec = node->costs;
777 row_index = src_node->solution;
778 col_index = tgt_node->solution;
780 vec = vector_copy(pbqp, node_vec);
783 vector_add_matrix_col(vec, src_mat, row_index);
785 vector_add_matrix_row(vec, src_mat, row_index);
789 vector_add_matrix_col(vec, tgt_mat, col_index);
791 vector_add_matrix_row(vec, tgt_mat, col_index);
794 node->solution = vector_get_min_index(vec);
795 if (pbqp->dump_file) {
796 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
799 obstack_free(&pbqp->obstack, vec);
802 int node_is_reduced(pbqp_node *node)
804 if (!reduced_bucket) return 0;
807 if (ARR_LEN(node->edges) == 0) return 1;
809 unsigned bucket_length = node_bucket_get_length(reduced_bucket);
810 unsigned bucket_index = node->bucket_index;
812 return bucket_index < bucket_length && reduced_bucket[bucket_index] == node;