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 /* Forward declarations. */
22 static void apply_Brute_Force(pbqp *pbqp);
24 static void insert_into_edge_bucket(pbqp_edge *edge)
26 if (edge_bucket_contains(edge_bucket, edge)) {
27 /* Edge is already inserted. */
31 edge_bucket_insert(&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 degree = pbqp_node_get_degree(node);
76 /* We have only one bucket for nodes with arity >= 3. */
81 node_bucket_insert(&node_buckets[degree], 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 = pbqp_node_get_degree(src_node);
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 = pbqp_node_get_degree(tgt_node);
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)
208 unsigned degree = pbqp_node_get_degree(node);
209 /* Assume node lost one incident edge. */
210 unsigned old_degree = degree + 1;
212 if (!buckets_filled) return;
214 /* Same bucket as before */
215 if (degree > 2) return;
217 if (!node_bucket_contains(node_buckets[old_degree], node)) {
218 /* Old arity is new arity, so we have nothing to do. */
219 assert(node_bucket_contains(node_buckets[degree], node));
223 /* Delete node from old bucket... */
224 node_bucket_remove(&node_buckets[old_degree], node);
226 /* ..and add to new one. */
227 node_bucket_insert(&node_buckets[degree], node);
230 static void check_melting_possibility(pbqp *pbqp, pbqp_edge *edge)
245 src_node = edge->src;
246 tgt_node = edge->tgt;
250 src_vec = src_node->costs;
251 tgt_vec = tgt_node->costs;
255 src_len = src_vec->len;
256 tgt_len = tgt_vec->len;
263 if (src_len == 1 && tgt_len == 1) {
264 //panic("Something is wrong");
268 for (src_index = 0; src_index < src_len; ++src_index) {
270 if (src_vec->entries[src_index].data == INF_COSTS) {
273 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
274 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
277 if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
286 if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
292 allRowsOk &= onlyOneZero;
296 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
298 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
301 for (src_index = 0; src_index < src_len; ++src_index) {
302 if (src_vec->entries[src_index].data == INF_COSTS) {
305 if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
314 if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
320 allColsOk &= onlyOneZero;
323 if (allRowsOk && allColsOk) {
328 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
341 src_node = edge->src;
342 tgt_node = edge->tgt;
346 /* If edge are already deleted, we have nothing to do. */
347 if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
350 if (pbqp->dump_file) {
352 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
353 dump_section(pbqp->dump_file, 3, txt);
356 src_vec = src_node->costs;
357 tgt_vec = tgt_node->costs;
361 src_len = src_vec->len;
362 tgt_len = tgt_vec->len;
369 if (pbqp->dump_file) {
370 fputs("Input:<br>\n", pbqp->dump_file);
371 dump_simplifyedge(pbqp, edge);
374 normalize_towards_source(pbqp, edge);
375 normalize_towards_target(pbqp, edge);
377 if (pbqp->dump_file) {
378 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
379 dump_simplifyedge(pbqp, edge);
382 if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
383 if (pbqp->dump_file) {
384 fputs("edge has been eliminated<br>\n", pbqp->dump_file);
388 reorder_node(src_node);
389 reorder_node(tgt_node);
391 //check_melting_possibility(pbqp, edge);
395 static void initial_simplify_edges(pbqp *pbqp)
402 if (pbqp->dump_file) {
403 pbqp_dump_input(pbqp);
404 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
407 node_len = pbqp->num_nodes;
411 /* First simplify all edges. */
412 for (node_index = 0; node_index < node_len; ++node_index) {
414 pbqp_node *node = get_node(pbqp, node_index);
421 edge_len = pbqp_node_get_degree(node);
423 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
424 pbqp_edge *edge = edges[edge_index];
426 /* Simplify only once per edge. */
427 if (node != edge->src) continue;
429 simplify_edge(pbqp, edge);
434 num determine_solution(FILE *file)
441 dump_section(file, 1, "4. Determine Solution/Minimum");
442 dump_section(file, 2, "4.1. Trivial Solution");
445 /* Solve trivial nodes and calculate solution. */
446 node_len = node_bucket_get_length(node_buckets[0]);
447 for (node_index = 0; node_index < node_len; ++node_index) {
448 pbqp_node *node = node_buckets[0][node_index];
451 node->solution = vector_get_min_index(node->costs);
452 solution = pbqp_add(solution,
453 node->costs->entries[node->solution].data);
455 fprintf(file, "node n%d is set to %d<br>\n", node->index, node->solution);
456 dump_node(file, node);
461 dump_section(file, 2, "Minimum");
462 fprintf(file, "Minimum is equal to %lld.", solution);
468 static void back_propagate(pbqp *pbqp)
471 unsigned node_len = node_bucket_get_length(reduced_bucket);
474 if (pbqp->dump_file) {
475 dump_section(pbqp->dump_file, 2, "Back Propagation");
478 for (node_index = node_len; node_index > 0; --node_index) {
479 pbqp_node *node = reduced_bucket[node_index - 1];
481 switch (pbqp_node_get_degree(node)) {
483 back_propagate_RI(pbqp, node);
486 back_propagate_RII(pbqp, node);
489 panic("Only nodes with degree one or two should be in this bucket");
495 static void apply_heuristic_reductions(pbqp *pbqp)
498 if (edge_bucket_get_length(edge_bucket) > 0) {
500 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
502 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
504 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
512 void solve_pbqp_heuristical(pbqp *pbqp)
514 /* Reduce nodes degree ... */
515 initial_simplify_edges(pbqp);
517 /* ... and put node into bucket representing their degree. */
518 fill_node_buckets(pbqp);
520 apply_heuristic_reductions(pbqp);
522 pbqp->solution = determine_solution(pbqp->dump_file);
524 /* Solve reduced nodes. */
525 back_propagate(pbqp);
530 void apply_edge(pbqp *pbqp)
532 pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
534 simplify_edge(pbqp, edge);
537 void apply_RI(pbqp *pbqp)
539 pbqp_node *node = node_bucket_pop(&node_buckets[1]);
540 pbqp_edge *edge = node->edges[0];
541 pbqp_matrix *mat = edge->costs;
542 int is_src = edge->src == node;
543 pbqp_node *other_node;
545 assert(pbqp_node_get_degree(node) == 1);
548 other_node = edge->tgt;
550 other_node = edge->src;
553 if (pbqp->dump_file) {
555 sprintf(txt, "RI-Reduction of Node n%d", node->index);
556 dump_section(pbqp->dump_file, 2, txt);
557 pbqp_dump_graph(pbqp);
558 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
559 dump_node(pbqp->dump_file, node);
560 dump_node(pbqp->dump_file, other_node);
561 dump_edge(pbqp->dump_file, edge);
565 pbqp_matrix_add_to_all_cols(mat, node->costs);
566 normalize_towards_target(pbqp, edge);
568 pbqp_matrix_add_to_all_rows(mat, node->costs);
569 normalize_towards_source(pbqp, edge);
571 disconnect_edge(other_node, edge);
573 if (pbqp->dump_file) {
574 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
575 dump_node(pbqp->dump_file, other_node);
578 reorder_node(other_node);
580 /* Add node to back propagation list. */
581 node_bucket_insert(&reduced_bucket, node);
584 void apply_RII(pbqp *pbqp)
586 pbqp_node *node = node_bucket_pop(&node_buckets[2]);
587 pbqp_edge *src_edge = node->edges[0];
588 pbqp_edge *tgt_edge = node->edges[1];
589 int src_is_src = src_edge->src == node;
590 int tgt_is_src = tgt_edge->src == node;
591 pbqp_matrix *src_mat;
592 pbqp_matrix *tgt_mat;
607 assert(pbqp_node_get_degree(node) == 2);
610 src_node = src_edge->tgt;
612 src_node = src_edge->src;
616 tgt_node = tgt_edge->tgt;
618 tgt_node = tgt_edge->src;
621 /* Swap nodes if necessary. */
622 if (tgt_node->index < src_node->index) {
634 src_is_src = src_edge->src == node;
635 tgt_is_src = tgt_edge->src == node;
638 if (pbqp->dump_file) {
640 sprintf(txt, "RII-Reduction of Node n%d", node->index);
641 dump_section(pbqp->dump_file, 2, txt);
642 pbqp_dump_graph(pbqp);
643 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
644 dump_node(pbqp->dump_file, src_node);
645 dump_edge(pbqp->dump_file, src_edge);
646 dump_node(pbqp->dump_file, node);
647 dump_edge(pbqp->dump_file, tgt_edge);
648 dump_node(pbqp->dump_file, tgt_node);
651 src_mat = src_edge->costs;
652 tgt_mat = tgt_edge->costs;
654 src_vec = src_node->costs;
655 tgt_vec = tgt_node->costs;
656 node_vec = node->costs;
658 row_len = src_vec->len;
659 col_len = tgt_vec->len;
660 node_len = node_vec->len;
662 mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
664 for (row_index = 0; row_index < row_len; ++row_index) {
665 for (col_index = 0; col_index < col_len; ++col_index) {
666 vec = vector_copy(pbqp, node_vec);
669 vector_add_matrix_col(vec, src_mat, row_index);
671 vector_add_matrix_row(vec, src_mat, row_index);
675 vector_add_matrix_col(vec, tgt_mat, col_index);
677 vector_add_matrix_row(vec, tgt_mat, col_index);
680 mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
682 obstack_free(&pbqp->obstack, vec);
686 pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
688 /* Disconnect node. */
689 disconnect_edge(src_node, src_edge);
690 disconnect_edge(tgt_node, tgt_edge);
692 /* Add node to back propagation list. */
693 node_bucket_insert(&reduced_bucket, node);
696 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
698 pbqp_matrix_add(edge->costs, mat);
700 /* Free local matrix. */
701 obstack_free(&pbqp->obstack, mat);
703 reorder_node(src_node);
704 reorder_node(tgt_node);
707 if (pbqp->dump_file) {
708 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
709 dump_edge(pbqp->dump_file, edge);
712 /* Edge has changed so we simplify it. */
713 simplify_edge(pbqp, edge);
716 static void select_alternative(pbqp_node *node, unsigned selected_index)
722 unsigned max_degree = pbqp_node_get_degree(node);
725 node->solution = selected_index;
726 node_vec = node->costs;
727 node_len = node_vec->len;
728 assert(selected_index < node_len);
730 /* Set all other costs to infinity. */
731 for (node_index = 0; node_index < node_len; ++node_index) {
732 if (node_index != selected_index) {
733 node_vec->entries[node_index].data = INF_COSTS;
737 /* Add all incident edges to edge bucket, since they are now independent. */
738 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
739 insert_into_edge_bucket(node->edges[edge_index]);
743 static pbqp_node *get_node_with_max_degree(void)
745 pbqp_node **bucket = node_buckets[3];
746 unsigned bucket_len = node_bucket_get_length(bucket);
747 unsigned bucket_index;
748 unsigned max_degree = 0;
749 pbqp_node *result = NULL;
751 for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
752 pbqp_node *candidate = bucket[bucket_index];
753 unsigned degree = pbqp_node_get_degree(candidate);
755 if (degree > max_degree) {
764 static unsigned get_local_minimal_alternative(pbqp *pbqp, pbqp_node *node)
771 unsigned max_degree = 0;
774 unsigned min_index = 0;
780 node_vec = node->costs;
781 node_len = node_vec->len;
783 for (node_index = 0; node_index < node_len; ++node_index) {
784 num value = node_vec->entries[node_index].data;
786 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
787 edge = node->edges[edge_index];
789 is_src = edge->src == node;
792 vec = vector_copy(pbqp, edge->tgt->costs);
793 vector_add_matrix_row(vec, mat, node_index);
795 vec = vector_copy(pbqp, edge->src->costs);
796 vector_add_matrix_col(vec, mat, node_index);
799 value = pbqp_add(value, vector_get_min(vec));
801 obstack_free(&pbqp->obstack, vec);
806 min_index = node_index;
813 void apply_RN(pbqp *pbqp)
815 pbqp_node *node = NULL;
816 unsigned min_index = 0;
820 /* We want to reduce a node with maximum degree. */
821 node = get_node_with_max_degree();
823 assert(pbqp_node_get_degree(node) > 2);
825 if (pbqp->dump_file) {
827 sprintf(txt, "RN-Reduction of Node n%d", node->index);
828 dump_section(pbqp->dump_file, 2, txt);
829 pbqp_dump_graph(pbqp);
832 min_index = get_local_minimal_alternative(pbqp, node);
834 if (pbqp->dump_file) {
835 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
836 node->index, min_index);
839 /* Now that we found the local minimum set all other costs to infinity. */
840 select_alternative(node, min_index);
843 static void apply_brute_force_reductions(pbqp *pbqp)
846 if (edge_bucket_get_length(edge_bucket) > 0) {
848 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
850 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
852 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
853 apply_Brute_Force(pbqp);
860 static unsigned get_minimal_alternative(pbqp *pbqp, pbqp_node *node)
865 unsigned min_index = 0;
867 unsigned bucket_index;
871 node_vec = node->costs;
872 node_len = node_vec->len;
873 bucket_index = node->bucket_index;
875 for (node_index = 0; node_index < node_len; ++node_index) {
876 pbqp_node_bucket bucket_deg3;
878 unsigned bucket_0_length;
879 unsigned bucket_red_length;
881 /* Some node buckets and the edge bucket should be empty. */
882 assert(node_bucket_get_length(node_buckets[1]) == 0);
883 assert(node_bucket_get_length(node_buckets[2]) == 0);
884 assert(edge_bucket_get_length(edge_bucket) == 0);
886 /* char *tmp = obstack_finish(&pbqp->obstack); */
888 /* Save current PBQP state. */
889 node_bucket_deep_copy(pbqp, &bucket_deg3, node_buckets[3]);
890 bucket_0_length = node_bucket_get_length(node_buckets[0]);
891 bucket_red_length = node_bucket_get_length(reduced_bucket);
893 /* Select alternative and solve PBQP recursively. */
894 select_alternative(node_buckets[3][bucket_index], node_index);
895 apply_brute_force_reductions(pbqp);
897 value = determine_solution(pbqp->dump_file);
901 min_index = node_index;
904 /* Some node buckets and the edge bucket should still be empty. */
905 assert(node_bucket_get_length(node_buckets[1]) == 0);
906 assert(node_bucket_get_length(node_buckets[2]) == 0);
907 assert(edge_bucket_get_length(edge_bucket) == 0);
909 /* Clear modified buckets... */
910 node_bucket_shrink(&node_buckets[3], 0);
912 /* ... and restore old PBQP state. */
913 node_bucket_shrink(&node_buckets[0], bucket_0_length);
914 node_bucket_shrink(&reduced_bucket, bucket_red_length);
915 node_bucket_copy(&node_buckets[3], bucket_deg3);
918 /* obstack_free(&pbqp->obstack, tmp); */
919 node_bucket_free(&bucket_deg3);
925 void apply_Brute_Force(pbqp *pbqp)
927 pbqp_node *node = NULL;
928 unsigned min_index = 0;
932 /* We want to reduce a node with maximum degree. */
933 node = get_node_with_max_degree();
935 assert(pbqp_node_get_degree(node) > 2);
937 if (pbqp->dump_file) {
939 sprintf(txt, "BF-Reduction of Node n%d", node->index);
940 dump_section(pbqp->dump_file, 2, txt);
941 pbqp_dump_graph(pbqp);
944 min_index = get_minimal_alternative(pbqp, node);
946 if (pbqp->dump_file) {
947 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
948 node->index, min_index);
951 /* Now that we found the minimum set all other costs to infinity. */
952 select_alternative(node, min_index);
955 void solve_pbqp_brute_force(pbqp *pbqp)
957 /* Reduce nodes degree ... */
958 initial_simplify_edges(pbqp);
960 /* ... and put node into bucket representing their degree. */
961 fill_node_buckets(pbqp);
963 apply_brute_force_reductions(pbqp);
965 pbqp->solution = determine_solution(pbqp->dump_file);
967 /* Solve reduced nodes. */
968 back_propagate(pbqp);
973 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
984 edge = node->edges[0];
986 is_src = edge->src == node;
992 vector_add_matrix_col(vec, mat, other->solution);
996 vector_add_matrix_row(vec, mat, other->solution);
999 node->solution = vector_get_min_index(vec);
1000 if (pbqp->dump_file) {
1001 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
1005 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
1007 pbqp_edge *src_edge = node->edges[0];
1008 pbqp_edge *tgt_edge = node->edges[1];
1009 int src_is_src = src_edge->src == node;
1010 int tgt_is_src = tgt_edge->src == node;
1011 pbqp_matrix *src_mat;
1012 pbqp_matrix *tgt_mat;
1013 pbqp_node *src_node;
1014 pbqp_node *tgt_node;
1023 src_node = src_edge->tgt;
1025 src_node = src_edge->src;
1029 tgt_node = tgt_edge->tgt;
1031 tgt_node = tgt_edge->src;
1034 /* Swap nodes if necessary. */
1035 if (tgt_node->index < src_node->index) {
1036 pbqp_node *tmp_node;
1037 pbqp_edge *tmp_edge;
1039 tmp_node = src_node;
1040 src_node = tgt_node;
1041 tgt_node = tmp_node;
1043 tmp_edge = src_edge;
1044 src_edge = tgt_edge;
1045 tgt_edge = tmp_edge;
1047 src_is_src = src_edge->src == node;
1048 tgt_is_src = tgt_edge->src == node;
1051 src_mat = src_edge->costs;
1052 tgt_mat = tgt_edge->costs;
1054 node_vec = node->costs;
1056 row_index = src_node->solution;
1057 col_index = tgt_node->solution;
1059 vec = vector_copy(pbqp, node_vec);
1062 vector_add_matrix_col(vec, src_mat, row_index);
1064 vector_add_matrix_row(vec, src_mat, row_index);
1068 vector_add_matrix_col(vec, tgt_mat, col_index);
1070 vector_add_matrix_row(vec, tgt_mat, col_index);
1073 node->solution = vector_get_min_index(vec);
1074 if (pbqp->dump_file) {
1075 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
1078 obstack_free(&pbqp->obstack, vec);
1081 int node_is_reduced(pbqp_node *node)
1083 if (!reduced_bucket) return 0;
1085 if (pbqp_node_get_degree(node) == 0) return 1;
1087 return node_bucket_contains(reduced_bucket, node);