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 if (edge_bucket_contains(edge_bucket, edge)) {
24 /* Edge is already inserted. */
28 edge_bucket_insert(&edge_bucket, edge);
31 static void init_buckets(void)
35 edge_bucket_init(&edge_bucket);
36 node_bucket_init(&reduced_bucket);
38 for (i = 0; i < 4; ++i) {
39 node_bucket_init(&node_buckets[i]);
43 static void free_buckets(void)
47 for (i = 0; i < 4; ++i) {
48 node_bucket_free(&node_buckets[i]);
51 edge_bucket_free(&edge_bucket);
52 node_bucket_free(&reduced_bucket);
57 static void fill_node_buckets(pbqp *pbqp)
63 node_len = pbqp->num_nodes;
65 for (node_index = 0; node_index < node_len; ++node_index) {
67 pbqp_node *node = get_node(pbqp, node_index);
71 arity = ARR_LEN(node->edges);
73 /* We have only one bucket for nodes with arity >= 3. */
78 node_bucket_insert(&node_buckets[arity], node);
84 static void normalize_towards_source(pbqp *pbqp, pbqp_edge *edge)
103 src_vec = src_node->costs;
104 tgt_vec = tgt_node->costs;
108 src_len = src_vec->len;
109 tgt_len = tgt_vec->len;
116 /* Normalize towards source node. */
117 for (src_index = 0; src_index < src_len; ++src_index) {
118 num min = pbqp_matrix_get_row_min(mat, src_index, tgt_vec);
121 if (src_vec->entries[src_index].data == INF_COSTS) {
122 pbqp_matrix_set_row_value(mat, src_index, 0);
124 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
126 src_vec->entries[src_index].data = pbqp_add(
127 src_vec->entries[src_index].data, min);
129 if (min == INF_COSTS) {
131 unsigned edge_len = ARR_LEN(src_node->edges);
133 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
134 pbqp_edge *edge_candidate = src_node->edges[edge_index];
135 if (edge_candidate != edge) {
136 insert_into_edge_bucket(edge_candidate);
144 static void normalize_towards_target(pbqp *pbqp, pbqp_edge *edge)
158 src_node = edge->src;
159 tgt_node = edge->tgt;
163 src_vec = src_node->costs;
164 tgt_vec = tgt_node->costs;
168 src_len = src_vec->len;
169 tgt_len = tgt_vec->len;
176 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
177 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
180 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
181 pbqp_matrix_set_col_value(mat, tgt_index, 0);
183 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
185 tgt_vec->entries[tgt_index].data = pbqp_add(
186 tgt_vec->entries[tgt_index].data, min);
188 if (min == INF_COSTS) {
190 unsigned edge_len = ARR_LEN(tgt_node->edges);
192 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
193 pbqp_edge *edge_candidate = tgt_node->edges[edge_index];
194 if (edge_candidate != edge) {
195 insert_into_edge_bucket(edge_candidate);
203 static void reorder_node(pbqp_node *node)
207 unsigned old_bucket_len;
208 unsigned old_bucket_index;
209 pbqp_node **old_bucket;
211 if (!buckets_filled) return;
215 arity = ARR_LEN(node->edges);
217 /* Same bucket as before */
218 if (arity > 2) return;
220 /* Assume node lost one incident edge. */
221 old_arity = arity + 1;
222 old_bucket = node_buckets[old_arity];
223 old_bucket_len = node_bucket_get_length(old_bucket);
224 old_bucket_index = node->bucket_index;
226 if (old_bucket_len <= old_bucket_index || old_bucket[old_bucket_index]
228 unsigned bucket_len = node_bucket_get_length(node_buckets[arity]);
230 /* Old arity is new arity, so we have nothing to do. */
231 assert(old_bucket_index < bucket_len);
232 assert(node_buckets[arity][old_bucket_index] == node);
236 assert(old_bucket[old_bucket_index] == node);
238 /* Delete node from old bucket... */
239 node_bucket_remove(&node_buckets[old_arity], node);
241 /* ..and add to new one. */
242 node->bucket_index = node_bucket_get_length(node_buckets[arity]);
243 ARR_APP1(pbqp_node*, node_buckets[arity], node);
246 static void check_melting_possibility(pbqp *pbqp, pbqp_edge *edge)
261 src_node = edge->src;
262 tgt_node = edge->tgt;
266 src_vec = src_node->costs;
267 tgt_vec = tgt_node->costs;
271 src_len = src_vec->len;
272 tgt_len = tgt_vec->len;
279 if (src_len == 1 && tgt_len == 1) {
280 //panic("Something is wrong");
284 for (src_index = 0; src_index < src_len; ++src_index) {
286 if (src_vec->entries[src_index].data == INF_COSTS) {
289 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
290 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
293 if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
302 if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
308 allRowsOk &= onlyOneZero;
312 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
314 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
317 for (src_index = 0; src_index < src_len; ++src_index) {
318 if (src_vec->entries[src_index].data == INF_COSTS) {
321 if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
330 if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
336 allColsOk &= onlyOneZero;
339 if (allRowsOk && allColsOk) {
344 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
357 src_node = edge->src;
358 tgt_node = edge->tgt;
362 /* If edge are already deleted, we have nothing to do. */
363 if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
366 if (pbqp->dump_file) {
368 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
369 dump_section(pbqp->dump_file, 3, txt);
372 src_vec = src_node->costs;
373 tgt_vec = tgt_node->costs;
377 src_len = src_vec->len;
378 tgt_len = tgt_vec->len;
385 if (pbqp->dump_file) {
386 fputs("Input:<br>\n", pbqp->dump_file);
387 dump_simplifyedge(pbqp, edge);
390 normalize_towards_source(pbqp, edge);
391 normalize_towards_target(pbqp, edge);
393 if (pbqp->dump_file) {
394 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
395 dump_simplifyedge(pbqp, edge);
398 if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
399 if (pbqp->dump_file) {
400 fputs("edge has been eliminated<br>\n", pbqp->dump_file);
404 reorder_node(src_node);
405 reorder_node(tgt_node);
407 //check_melting_possibility(pbqp, edge);
411 void solve_pbqp_heuristical(pbqp *pbqp)
418 if (pbqp->dump_file) {
419 pbqp_dump_input(pbqp);
420 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
423 node_len = pbqp->num_nodes;
427 /* First simplify all edges. */
428 for (node_index = 0; node_index < node_len; ++node_index) {
430 pbqp_node *node = get_node(pbqp, node_index);
437 edge_len = ARR_LEN(edges);
439 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
440 pbqp_edge *edge = edges[edge_index];
442 /* Simplify only once per edge. */
443 if (node != edge->src) continue;
445 simplify_edge(pbqp, edge);
449 /* Put node into bucket representing their arity. */
450 fill_node_buckets(pbqp);
453 if (edge_bucket_get_length(edge_bucket) > 0) {
455 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
457 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
459 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
466 if (pbqp->dump_file) {
467 dump_section(pbqp->dump_file, 1, "4. Determine Solution/Minimum");
468 dump_section(pbqp->dump_file, 2, "4.1. Trivial Solution");
471 /* Solve trivial nodes and calculate solution. */
472 node_len = node_bucket_get_length(node_buckets[0]);
473 for (node_index = 0; node_index < node_len; ++node_index) {
474 pbqp_node *node = node_buckets[0][node_index];
477 node->solution = vector_get_min_index(node->costs);
478 pbqp->solution = pbqp_add(pbqp->solution,
479 node->costs->entries[node->solution].data);
480 if (pbqp->dump_file) {
481 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
482 dump_node(pbqp, node);
486 if (pbqp->dump_file) {
487 dump_section(pbqp->dump_file, 2, "Minimum");
488 fprintf(pbqp->dump_file, "Minimum is equal to %lld.", pbqp->solution);
489 dump_section(pbqp->dump_file, 2, "Back Propagation");
492 /* Solve reduced nodes. */
493 node_len = node_bucket_get_length(reduced_bucket);
494 for (node_index = node_len; node_index > 0; --node_index) {
495 pbqp_node *node = reduced_bucket[node_index - 1];
498 switch (ARR_LEN(node->edges)) {
500 back_propagate_RI(pbqp, node);
503 back_propagate_RII(pbqp, node);
506 panic("Only nodes with degree one or two should be in this bucket");
514 void apply_edge(pbqp *pbqp)
516 pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
518 simplify_edge(pbqp, edge);
521 void apply_RI(pbqp *pbqp)
523 pbqp_node *node = node_bucket_pop(&node_buckets[1]);
524 pbqp_edge *edge = node->edges[0];
525 pbqp_matrix *mat = edge->costs;
526 int is_src = edge->src == node;
527 pbqp_node *other_node;
530 other_node = edge->tgt;
532 other_node = edge->src;
535 if (pbqp->dump_file) {
537 sprintf(txt, "RI-Reduction of Node n%d", node->index);
538 dump_section(pbqp->dump_file, 2, txt);
539 pbqp_dump_graph(pbqp);
540 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
541 dump_node(pbqp, node);
542 dump_node(pbqp, other_node);
543 dump_edge(pbqp, edge);
547 pbqp_matrix_add_to_all_cols(mat, node->costs);
548 normalize_towards_target(pbqp, edge);
550 pbqp_matrix_add_to_all_rows(mat, node->costs);
551 normalize_towards_source(pbqp, edge);
553 disconnect_edge(other_node, edge);
555 if (pbqp->dump_file) {
556 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
557 dump_node(pbqp, other_node);
560 reorder_node(other_node);
562 /* Add node to back propagation list. */
563 node_bucket_insert(&reduced_bucket, node);
566 void apply_RII(pbqp *pbqp)
568 pbqp_node *node = node_bucket_pop(&node_buckets[2]);
569 pbqp_edge *src_edge = node->edges[0];
570 pbqp_edge *tgt_edge = node->edges[1];
571 int src_is_src = src_edge->src == node;
572 int tgt_is_src = tgt_edge->src == node;
573 pbqp_matrix *src_mat;
574 pbqp_matrix *tgt_mat;
591 src_node = src_edge->tgt;
593 src_node = src_edge->src;
597 tgt_node = tgt_edge->tgt;
599 tgt_node = tgt_edge->src;
602 /* Swap nodes if necessary. */
603 if (tgt_node->index < src_node->index) {
615 src_is_src = src_edge->src == node;
616 tgt_is_src = tgt_edge->src == node;
619 if (pbqp->dump_file) {
621 sprintf(txt, "RII-Reduction of Node n%d", node->index);
622 dump_section(pbqp->dump_file, 2, txt);
623 pbqp_dump_graph(pbqp);
624 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
625 dump_node(pbqp, src_node);
626 dump_edge(pbqp, src_edge);
627 dump_node(pbqp, node);
628 dump_edge(pbqp, tgt_edge);
629 dump_node(pbqp, tgt_node);
632 src_mat = src_edge->costs;
633 tgt_mat = tgt_edge->costs;
635 src_vec = src_node->costs;
636 tgt_vec = tgt_node->costs;
637 node_vec = node->costs;
639 row_len = src_vec->len;
640 col_len = tgt_vec->len;
641 node_len = node_vec->len;
643 mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
645 for (row_index = 0; row_index < row_len; ++row_index) {
646 for (col_index = 0; col_index < col_len; ++col_index) {
647 vec = vector_copy(pbqp, node_vec);
650 vector_add_matrix_col(vec, src_mat, row_index);
652 vector_add_matrix_row(vec, src_mat, row_index);
656 vector_add_matrix_col(vec, tgt_mat, col_index);
658 vector_add_matrix_row(vec, tgt_mat, col_index);
661 mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
663 obstack_free(&pbqp->obstack, vec);
667 pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
669 /* Disconnect node. */
670 disconnect_edge(src_node, src_edge);
671 disconnect_edge(tgt_node, tgt_edge);
673 /* Add node to back propagation list. */
674 node_bucket_insert(&reduced_bucket, node);
677 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
679 pbqp_matrix_add(edge->costs, mat);
681 /* Free local matrix. */
682 obstack_free(&pbqp->obstack, mat);
684 reorder_node(src_node);
685 reorder_node(tgt_node);
688 if (pbqp->dump_file) {
689 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
690 dump_edge(pbqp, edge);
693 /* Edge has changed so we simplify it. */
694 simplify_edge(pbqp, edge);
697 void apply_RN(pbqp *pbqp)
699 pbqp_node **bucket = node_buckets[3];
700 unsigned bucket_len = node_bucket_get_length(bucket);
701 unsigned bucket_index;
702 pbqp_node *node = NULL;
708 unsigned max_degree = 0;
711 unsigned min_index = 0;
717 /* Search for node with maximum degree. */
718 for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
719 pbqp_node *candidate = bucket[bucket_index];
720 unsigned degree = ARR_LEN(candidate->edges);
722 if (degree > max_degree) {
728 node_vec = node->costs;
729 node_len = node_vec->len;
731 if (pbqp->dump_file) {
733 sprintf(txt, "RN-Reduction of Node n%d", node->index);
734 dump_section(pbqp->dump_file, 2, txt);
735 pbqp_dump_graph(pbqp);
738 for (node_index = 0; node_index < node_len; ++node_index) {
739 num value = node_vec->entries[node_index].data;
741 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
742 edge = node->edges[edge_index];
744 is_src = edge->src == node;
747 vec = vector_copy(pbqp, edge->tgt->costs);
748 vector_add_matrix_row(vec, mat, node_index);
750 vec = vector_copy(pbqp, edge->src->costs);
751 vector_add_matrix_col(vec, mat, node_index);
754 value = pbqp_add(value, vector_get_min(vec));
756 obstack_free(&pbqp->obstack, vec);
761 min_index = node_index;
765 if (pbqp->dump_file) {
766 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
767 node->index, min_index);
768 fprintf(pbqp->dump_file, "Minimal cost of RN reduction: %lld<br>\n",
772 node->solution = min_index;
774 /* Now that we found the local minimum set all other costs to infinity. */
775 for (node_index = 0; node_index < node_len; ++node_index) {
776 if (node_index != min_index) {
777 node_vec->entries[node_index].data = INF_COSTS;
781 /* Add all incident edges to edge bucket, since they are now independent. */
782 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
783 insert_into_edge_bucket(node->edges[edge_index]);
787 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
798 edge = node->edges[0];
800 is_src = edge->src == node;
806 vector_add_matrix_col(vec, mat, other->solution);
810 vector_add_matrix_row(vec, mat, other->solution);
813 node->solution = vector_get_min_index(vec);
814 if (pbqp->dump_file) {
815 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
819 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
821 pbqp_edge *src_edge = node->edges[0];
822 pbqp_edge *tgt_edge = node->edges[1];
823 int src_is_src = src_edge->src == node;
824 int tgt_is_src = tgt_edge->src == node;
825 pbqp_matrix *src_mat;
826 pbqp_matrix *tgt_mat;
837 src_node = src_edge->tgt;
839 src_node = src_edge->src;
843 tgt_node = tgt_edge->tgt;
845 tgt_node = tgt_edge->src;
848 /* Swap nodes if necessary. */
849 if (tgt_node->index < src_node->index) {
861 src_is_src = src_edge->src == node;
862 tgt_is_src = tgt_edge->src == node;
865 src_mat = src_edge->costs;
866 tgt_mat = tgt_edge->costs;
868 node_vec = node->costs;
870 row_index = src_node->solution;
871 col_index = tgt_node->solution;
873 vec = vector_copy(pbqp, node_vec);
876 vector_add_matrix_col(vec, src_mat, row_index);
878 vector_add_matrix_row(vec, src_mat, row_index);
882 vector_add_matrix_col(vec, tgt_mat, col_index);
884 vector_add_matrix_row(vec, tgt_mat, col_index);
887 node->solution = vector_get_min_index(vec);
888 if (pbqp->dump_file) {
889 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
892 obstack_free(&pbqp->obstack, vec);
895 int node_is_reduced(pbqp_node *node)
897 if (!reduced_bucket) return 0;
900 if (ARR_LEN(node->edges) == 0) return 1;
902 return node_bucket_contains(reduced_bucket, node);