nsz Git - libfirm/blob - heuristical.c

   1 #include "adt/array.h"
   2 #include "assert.h"
   3 #include "error.h"
   4
   5 #include "bucket.h"
   6 #include "heuristical.h"
   7 #include "html_dumper.h"
   8 #include "kaps.h"
   9 #include "matrix.h"
  10 #include "pbqp_edge.h"
  11 #include "pbqp_edge_t.h"
  12 #include "pbqp_node.h"
  13 #include "pbqp_node_t.h"
  14 #include "vector.h"
  15
  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;
  20
  21 static void insert_into_edge_bucket(pbqp_edge *edge)
  22 {
  23         if (edge_bucket_contains(edge_bucket, edge)) {
  24                 /* Edge is already inserted. */
  25                 return;
  26         }
  27
  28         edge_bucket_insert(&edge_bucket, edge);
  29 }
  30
  31 static void init_buckets(void)
  32 {
  33         int i;
  34
  35         edge_bucket_init(&edge_bucket);
  36         node_bucket_init(&reduced_bucket);
  37
  38         for (i = 0; i < 4; ++i) {
  39                 node_bucket_init(&node_buckets[i]);
  40         }
  41 }
  42
  43 static void free_buckets(void)
  44 {
  45         int i;
  46
  47         for (i = 0; i < 4; ++i) {
  48                 node_bucket_free(&node_buckets[i]);
  49         }
  50
  51         edge_bucket_free(&edge_bucket);
  52         node_bucket_free(&reduced_bucket);
  53
  54         buckets_filled = 0;
  55 }
  56
  57 static void fill_node_buckets(pbqp *pbqp)
  58 {
  59         unsigned node_index;
  60         unsigned node_len;
  61
  62         assert(pbqp);
  63         node_len = pbqp->num_nodes;
  64
  65         for (node_index = 0; node_index < node_len; ++node_index) {
  66                 unsigned   degree;
  67                 pbqp_node *node = get_node(pbqp, node_index);
  68
  69                 if (!node) continue;
  70
  71                 degree = pbqp_node_get_degree(node);
  72
  73                 /* We have only one bucket for nodes with arity >= 3. */
  74                 if (degree > 3) {
  75                         degree = 3;
  76                 }
  77
  78                 node_bucket_insert(&node_buckets[degree], node);
  79         }
  80
  81         buckets_filled = 1;
  82 }
  83
  84 static void normalize_towards_source(pbqp *pbqp, pbqp_edge *edge)
  85 {
  86         pbqp_matrix    *mat;
  87         pbqp_node      *src_node;
  88         pbqp_node      *tgt_node;
  89         vector         *src_vec;
  90         vector         *tgt_vec;
  91         int             src_len;
  92         int             tgt_len;
  93         int             src_index;
  94
  95         assert(pbqp);
  96         assert(edge);
  97
  98         src_node = edge->src;
  99         tgt_node = edge->tgt;
 100         assert(src_node);
 101         assert(tgt_node);
 102
 103         src_vec = src_node->costs;
 104         tgt_vec = tgt_node->costs;
 105         assert(src_vec);
 106         assert(tgt_vec);
 107
 108         src_len = src_vec->len;
 109         tgt_len = tgt_vec->len;
 110         assert(src_len > 0);
 111         assert(tgt_len > 0);
 112
 113         mat = edge->costs;
 114         assert(mat);
 115
 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);
 119
 120                 if (min != 0) {
 121                         if (src_vec->entries[src_index].data == INF_COSTS) {
 122                                 pbqp_matrix_set_row_value(mat, src_index, 0);
 123                         } else {
 124                                 pbqp_matrix_sub_row_value(mat, src_index, tgt_vec, min);
 125                         }
 126                         src_vec->entries[src_index].data = pbqp_add(
 127                                         src_vec->entries[src_index].data, min);
 128
 129                         if (min == INF_COSTS) {
 130                                 unsigned edge_index;
 131                                 unsigned edge_len = pbqp_node_get_degree(src_node);
 132
 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);
 137                                         }
 138                                 }
 139                         }
 140                 }
 141         }
 142 }
 143
 144 static void normalize_towards_target(pbqp *pbqp, pbqp_edge *edge)
 145 {
 146         pbqp_matrix    *mat;
 147         pbqp_node      *src_node;
 148         pbqp_node      *tgt_node;
 149         vector         *src_vec;
 150         vector         *tgt_vec;
 151         int             src_len;
 152         int             tgt_len;
 153         int             tgt_index;
 154
 155         assert(pbqp);
 156         assert(edge);
 157
 158         src_node = edge->src;
 159         tgt_node = edge->tgt;
 160         assert(src_node);
 161         assert(tgt_node);
 162
 163         src_vec = src_node->costs;
 164         tgt_vec = tgt_node->costs;
 165         assert(src_vec);
 166         assert(tgt_vec);
 167
 168         src_len = src_vec->len;
 169         tgt_len = tgt_vec->len;
 170         assert(src_len > 0);
 171         assert(tgt_len > 0);
 172
 173         mat = edge->costs;
 174         assert(mat);
 175
 176         for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 177                 num min = pbqp_matrix_get_col_min(mat, tgt_index, src_vec);
 178
 179                 if (min != 0) {
 180                         if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 181                                 pbqp_matrix_set_col_value(mat, tgt_index, 0);
 182                         } else {
 183                                 pbqp_matrix_sub_col_value(mat, tgt_index, src_vec, min);
 184                         }
 185                         tgt_vec->entries[tgt_index].data = pbqp_add(
 186                                         tgt_vec->entries[tgt_index].data, min);
 187
 188                         if (min == INF_COSTS) {
 189                                 unsigned edge_index;
 190                                 unsigned edge_len = pbqp_node_get_degree(tgt_node);
 191
 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);
 196                                         }
 197                                 }
 198                         }
 199                 }
 200         }
 201 }
 202
 203 static void reorder_node(pbqp_node *node)
 204 {
 205         unsigned    degree     = pbqp_node_get_degree(node);
 206         /* Assume node lost one incident edge. */
 207         unsigned    old_degree = degree + 1;
 208
 209         if (!buckets_filled) return;
 210
 211         /* Same bucket as before */
 212         if (degree > 2) return;
 213
 214         if (!node_bucket_contains(node_buckets[old_degree], node)) {
 215                 /* Old arity is new arity, so we have nothing to do. */
 216                 assert(node_bucket_contains(node_buckets[degree], node));
 217                 return;
 218         }
 219
 220         /* Delete node from old bucket... */
 221         node_bucket_remove(&node_buckets[old_degree], node);
 222
 223         /* ..and add to new one. */
 224         node_bucket_insert(&node_buckets[degree], node);
 225 }
 226
 227 static void check_melting_possibility(pbqp *pbqp, pbqp_edge *edge)
 228 {
 229         pbqp_matrix    *mat;
 230         pbqp_node      *src_node;
 231         pbqp_node      *tgt_node;
 232         vector         *src_vec;
 233         vector         *tgt_vec;
 234         int             src_len;
 235         int             tgt_len;
 236         int             src_index;
 237         int             tgt_index;
 238
 239         assert(pbqp);
 240         assert(edge);
 241
 242         src_node = edge->src;
 243         tgt_node = edge->tgt;
 244         assert(src_node);
 245         assert(tgt_node);
 246
 247         src_vec = src_node->costs;
 248         tgt_vec = tgt_node->costs;
 249         assert(src_vec);
 250         assert(tgt_vec);
 251
 252         src_len = src_vec->len;
 253         tgt_len = tgt_vec->len;
 254         assert(src_len > 0);
 255         assert(tgt_len > 0);
 256
 257         mat = edge->costs;
 258         assert(mat);
 259
 260         if (src_len == 1 && tgt_len == 1) {
 261                 //panic("Something is wrong");
 262         }
 263
 264         int allRowsOk = 1;
 265         for (src_index = 0; src_index < src_len; ++src_index) {
 266                 int onlyOneZero = 0;
 267                 if (src_vec->entries[src_index].data == INF_COSTS) {
 268                         continue;
 269                 }
 270                 for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 271                         if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 272                                 continue;
 273                         }
 274                         if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
 275                                 if (onlyOneZero) {
 276                                         onlyOneZero = 0;
 277                                         break;
 278                                 } else {
 279                                         onlyOneZero = 1;
 280                                         continue;
 281                                 }
 282                         }
 283                         if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
 284                                 continue;
 285                         }
 286                         onlyOneZero = 0;
 287                         break;
 288                 }
 289                 allRowsOk &= onlyOneZero;
 290         }
 291
 292         int allColsOk = 1;
 293         for (tgt_index = 0; tgt_index < tgt_len; ++tgt_index) {
 294                 int onlyOneZero = 0;
 295                 if (tgt_vec->entries[tgt_index].data == INF_COSTS) {
 296                         continue;
 297                 }
 298                 for (src_index = 0; src_index < src_len; ++src_index) {
 299                         if (src_vec->entries[src_index].data == INF_COSTS) {
 300                                 continue;
 301                         }
 302                         if (mat->entries[src_index * tgt_len + tgt_index] == 0) {
 303                                 if (onlyOneZero) {
 304                                         onlyOneZero = 0;
 305                                         break;
 306                                 } else {
 307                                         onlyOneZero = 1;
 308                                         continue;
 309                                 }
 310                         }
 311                         if (mat->entries[src_index * tgt_len + tgt_index] == INF_COSTS) {
 312                                 continue;
 313                         }
 314                         onlyOneZero = 0;
 315                         break;
 316                 }
 317                 allColsOk &= onlyOneZero;
 318         }
 319
 320         if (allRowsOk && allColsOk) {
 321                 panic("Hurray");
 322         }
 323 }
 324
 325 static void simplify_edge(pbqp *pbqp, pbqp_edge *edge)
 326 {
 327         pbqp_matrix    *mat;
 328         pbqp_node      *src_node;
 329         pbqp_node      *tgt_node;
 330         vector         *src_vec;
 331         vector         *tgt_vec;
 332         int             src_len;
 333         int             tgt_len;
 334
 335         assert(pbqp);
 336         assert(edge);
 337
 338         src_node = edge->src;
 339         tgt_node = edge->tgt;
 340         assert(src_node);
 341         assert(tgt_node);
 342
 343         /* If edge are already deleted, we have nothing to do. */
 344         if (!is_connected(src_node, edge) || !is_connected(tgt_node, edge))
 345                 return;
 346
 347         if (pbqp->dump_file) {
 348                 char txt[100];
 349                 sprintf(txt, "Simplification of Edge n%d-n%d", src_node->index, tgt_node->index);
 350                 dump_section(pbqp->dump_file, 3, txt);
 351         }
 352
 353         src_vec = src_node->costs;
 354         tgt_vec = tgt_node->costs;
 355         assert(src_vec);
 356         assert(tgt_vec);
 357
 358         src_len = src_vec->len;
 359         tgt_len = tgt_vec->len;
 360         assert(src_len > 0);
 361         assert(tgt_len > 0);
 362
 363         mat = edge->costs;
 364         assert(mat);
 365
 366         if (pbqp->dump_file) {
 367                 fputs("Input:<br>\n", pbqp->dump_file);
 368                 dump_simplifyedge(pbqp, edge);
 369         }
 370
 371         normalize_towards_source(pbqp, edge);
 372         normalize_towards_target(pbqp, edge);
 373
 374         if (pbqp->dump_file) {
 375                 fputs("<br>\nOutput:<br>\n", pbqp->dump_file);
 376                 dump_simplifyedge(pbqp, edge);
 377         }
 378
 379         if (pbqp_matrix_is_zero(mat, src_vec, tgt_vec)) {
 380                 if (pbqp->dump_file) {
 381                         fputs("edge has been eliminated<br>\n", pbqp->dump_file);
 382                 }
 383
 384                 delete_edge(edge);
 385                 reorder_node(src_node);
 386                 reorder_node(tgt_node);
 387         } else {
 388                 //check_melting_possibility(pbqp, edge);
 389         }
 390 }
 391
 392 static void initial_simplify_edges(pbqp *pbqp)
 393 {
 394         unsigned node_index;
 395         unsigned node_len;
 396
 397         assert(pbqp);
 398
 399         if (pbqp->dump_file) {
 400                 pbqp_dump_input(pbqp);
 401                 dump_section(pbqp->dump_file, 1, "2. Simplification of Cost Matrices");
 402         }
 403
 404         node_len = pbqp->num_nodes;
 405
 406         init_buckets();
 407
 408         /* First simplify all edges. */
 409         for (node_index = 0; node_index < node_len; ++node_index) {
 410                 unsigned    edge_index;
 411                 pbqp_node  *node = get_node(pbqp, node_index);
 412                 pbqp_edge **edges;
 413                 unsigned    edge_len;
 414
 415                 if (!node) continue;
 416
 417                 edges = node->edges;
 418                 edge_len = pbqp_node_get_degree(node);
 419
 420                 for (edge_index = 0; edge_index < edge_len; ++edge_index) {
 421                         pbqp_edge *edge = edges[edge_index];
 422
 423                         /* Simplify only once per edge. */
 424                         if (node != edge->src) continue;
 425
 426                         simplify_edge(pbqp, edge);
 427                 }
 428         }
 429 }
 430
 431 num determine_solution(FILE *file)
 432 {
 433         unsigned node_index;
 434         unsigned node_len;
 435         num      solution;
 436
 437         if (file) {
 438                 dump_section(file, 1, "4. Determine Solution/Minimum");
 439                 dump_section(file, 2, "4.1. Trivial Solution");
 440         }
 441
 442         /* Solve trivial nodes and calculate solution. */
 443         node_len = node_bucket_get_length(node_buckets[0]);
 444         for (node_index = 0; node_index < node_len; ++node_index) {
 445                 pbqp_node *node = node_buckets[0][node_index];
 446                 assert(node);
 447
 448                 node->solution = vector_get_min_index(node->costs);
 449                 solution       = pbqp_add(solution,
 450                                 node->costs->entries[node->solution].data);
 451                 if (file) {
 452                         fprintf(file, "node n%d is set to %d<br>\n", node->index, node->solution);
 453                         dump_node(file, node);
 454                 }
 455         }
 456
 457         if (file) {
 458                 dump_section(file, 2, "Minimum");
 459                 fprintf(file, "Minimum is equal to %lld.", solution);
 460         }
 461
 462         return solution;
 463 }
 464
 465 static void back_propagate(pbqp *pbqp)
 466 {
 467         unsigned node_index;
 468         unsigned node_len   = node_bucket_get_length(reduced_bucket);
 469
 470         assert(pbqp);
 471         if (pbqp->dump_file) {
 472                 dump_section(pbqp->dump_file, 2, "Back Propagation");
 473         }
 474
 475         for (node_index = node_len; node_index > 0; --node_index) {
 476                 pbqp_node *node = reduced_bucket[node_index - 1];
 477
 478                 switch (pbqp_node_get_degree(node)) {
 479                         case 1:
 480                                 back_propagate_RI(pbqp, node);
 481                                 break;
 482                         case 2:
 483                                 back_propagate_RII(pbqp, node);
 484                                 break;
 485                         default:
 486                                 panic("Only nodes with degree one or two should be in this bucket");
 487                                 break;
 488                 }
 489         }
 490 }
 491
 492 void solve_pbqp_heuristical(pbqp *pbqp)
 493 {
 494         /* Reduce nodes degree ... */
 495         initial_simplify_edges(pbqp);
 496
 497         /* ... and put node into bucket representing their degree. */
 498         fill_node_buckets(pbqp);
 499
 500         for (;;) {
 501                 if (edge_bucket_get_length(edge_bucket) > 0) {
 502                         apply_edge(pbqp);
 503                 } else if (node_bucket_get_length(node_buckets[1]) > 0) {
 504                         apply_RI(pbqp);
 505                 } else if (node_bucket_get_length(node_buckets[2]) > 0) {
 506                         apply_RII(pbqp);
 507                 } else if (node_bucket_get_length(node_buckets[3]) > 0) {
 508                         apply_RN(pbqp);
 509                 } else {
 510                         break;
 511                 }
 512         }
 513
 514         pbqp->solution = determine_solution(pbqp->dump_file);
 515
 516         /* Solve reduced nodes. */
 517         back_propagate(pbqp);
 518
 519         free_buckets();
 520 }
 521
 522 void apply_edge(pbqp *pbqp)
 523 {
 524         pbqp_edge *edge = edge_bucket_pop(&edge_bucket);
 525
 526         simplify_edge(pbqp, edge);
 527 }
 528
 529 void apply_RI(pbqp *pbqp)
 530 {
 531         pbqp_node   *node       = node_bucket_pop(&node_buckets[1]);
 532         pbqp_edge   *edge       = node->edges[0];
 533         pbqp_matrix *mat        = edge->costs;
 534         int          is_src     = edge->src == node;
 535         pbqp_node   *other_node;
 536
 537         if (is_src) {
 538                 other_node = edge->tgt;
 539         } else {
 540                 other_node = edge->src;
 541         }
 542
 543         if (pbqp->dump_file) {
 544                 char     txt[100];
 545                 sprintf(txt, "RI-Reduction of Node n%d", node->index);
 546                 dump_section(pbqp->dump_file, 2, txt);
 547                 pbqp_dump_graph(pbqp);
 548                 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
 549                 dump_node(pbqp->dump_file, node);
 550                 dump_node(pbqp->dump_file, other_node);
 551                 dump_edge(pbqp->dump_file, edge);
 552         }
 553
 554         if (is_src) {
 555                 pbqp_matrix_add_to_all_cols(mat, node->costs);
 556                 normalize_towards_target(pbqp, edge);
 557         } else {
 558                 pbqp_matrix_add_to_all_rows(mat, node->costs);
 559                 normalize_towards_source(pbqp, edge);
 560         }
 561         disconnect_edge(other_node, edge);
 562
 563         if (pbqp->dump_file) {
 564                 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
 565                 dump_node(pbqp->dump_file, other_node);
 566         }
 567
 568         reorder_node(other_node);
 569
 570         /* Add node to back propagation list. */
 571         node_bucket_insert(&reduced_bucket, node);
 572 }
 573
 574 void apply_RII(pbqp *pbqp)
 575 {
 576         pbqp_node   *node       = node_bucket_pop(&node_buckets[2]);
 577         pbqp_edge   *src_edge   = node->edges[0];
 578         pbqp_edge   *tgt_edge   = node->edges[1];
 579         int          src_is_src = src_edge->src == node;
 580         int          tgt_is_src = tgt_edge->src == node;
 581         pbqp_matrix *src_mat;
 582         pbqp_matrix *tgt_mat;
 583         pbqp_node   *src_node;
 584         pbqp_node   *tgt_node;
 585         pbqp_matrix *mat;
 586         vector      *vec;
 587         vector      *node_vec;
 588         vector      *src_vec;
 589         vector      *tgt_vec;
 590         unsigned     col_index;
 591         unsigned     col_len;
 592         unsigned     row_index;
 593         unsigned     row_len;
 594         unsigned     node_len;
 595
 596         assert(pbqp);
 597
 598         if (src_is_src) {
 599                 src_node = src_edge->tgt;
 600         } else {
 601                 src_node = src_edge->src;
 602         }
 603
 604         if (tgt_is_src) {
 605                 tgt_node = tgt_edge->tgt;
 606         } else {
 607                 tgt_node = tgt_edge->src;
 608         }
 609
 610         /* Swap nodes if necessary. */
 611         if (tgt_node->index < src_node->index) {
 612                 pbqp_node *tmp_node;
 613                 pbqp_edge *tmp_edge;
 614
 615                 tmp_node = src_node;
 616                 src_node = tgt_node;
 617                 tgt_node = tmp_node;
 618
 619                 tmp_edge = src_edge;
 620                 src_edge = tgt_edge;
 621                 tgt_edge = tmp_edge;
 622
 623                 src_is_src = src_edge->src == node;
 624                 tgt_is_src = tgt_edge->src == node;
 625         }
 626
 627         if (pbqp->dump_file) {
 628                 char     txt[100];
 629                 sprintf(txt, "RII-Reduction of Node n%d", node->index);
 630                 dump_section(pbqp->dump_file, 2, txt);
 631                 pbqp_dump_graph(pbqp);
 632                 fputs("<br>\nBefore reduction:<br>\n", pbqp->dump_file);
 633                 dump_node(pbqp->dump_file, src_node);
 634                 dump_edge(pbqp->dump_file, src_edge);
 635                 dump_node(pbqp->dump_file, node);
 636                 dump_edge(pbqp->dump_file, tgt_edge);
 637                 dump_node(pbqp->dump_file, tgt_node);
 638         }
 639
 640         src_mat = src_edge->costs;
 641         tgt_mat = tgt_edge->costs;
 642
 643         src_vec  = src_node->costs;
 644         tgt_vec  = tgt_node->costs;
 645         node_vec = node->costs;
 646
 647         row_len  = src_vec->len;
 648         col_len  = tgt_vec->len;
 649         node_len = node_vec->len;
 650
 651         mat = pbqp_matrix_alloc(pbqp, row_len, col_len);
 652
 653         for (row_index = 0; row_index < row_len; ++row_index) {
 654                 for (col_index = 0; col_index < col_len; ++col_index) {
 655                         vec = vector_copy(pbqp, node_vec);
 656
 657                         if (src_is_src) {
 658                                 vector_add_matrix_col(vec, src_mat, row_index);
 659                         } else {
 660                                 vector_add_matrix_row(vec, src_mat, row_index);
 661                         }
 662
 663                         if (tgt_is_src) {
 664                                 vector_add_matrix_col(vec, tgt_mat, col_index);
 665                         } else {
 666                                 vector_add_matrix_row(vec, tgt_mat, col_index);
 667                         }
 668
 669                         mat->entries[row_index * col_len + col_index] = vector_get_min(vec);
 670
 671                         obstack_free(&pbqp->obstack, vec);
 672                 }
 673         }
 674
 675         pbqp_edge *edge = get_edge(pbqp, src_node->index, tgt_node->index);
 676
 677         /* Disconnect node. */
 678         disconnect_edge(src_node, src_edge);
 679         disconnect_edge(tgt_node, tgt_edge);
 680
 681         /* Add node to back propagation list. */
 682         node_bucket_insert(&reduced_bucket, node);
 683
 684         if (edge == NULL) {
 685                 edge = alloc_edge(pbqp, src_node->index, tgt_node->index, mat);
 686         } else {
 687                 pbqp_matrix_add(edge->costs, mat);
 688
 689                 /* Free local matrix. */
 690                 obstack_free(&pbqp->obstack, mat);
 691
 692                 reorder_node(src_node);
 693                 reorder_node(tgt_node);
 694         }
 695
 696         if (pbqp->dump_file) {
 697                 fputs("<br>\nAfter reduction:<br>\n", pbqp->dump_file);
 698                 dump_edge(pbqp->dump_file, edge);
 699         }
 700
 701         /* Edge has changed so we simplify it. */
 702         simplify_edge(pbqp, edge);
 703 }
 704
 705 static void select_alternative(pbqp_node *node, unsigned selected_index)
 706 {
 707         unsigned  edge_index;
 708         unsigned  node_index;
 709         unsigned  node_len;
 710         vector   *node_vec;
 711         unsigned  max_degree = pbqp_node_get_degree(node);
 712
 713         assert(selected_index < max_degree);
 714         assert(node);
 715         node->solution = selected_index;
 716         node_vec = node->costs;
 717         node_len = node_vec->len;
 718
 719         /* Set all other costs to infinity. */
 720         for (node_index = 0; node_index < node_len; ++node_index) {
 721                 if (node_index != selected_index) {
 722                         node_vec->entries[node_index].data = INF_COSTS;
 723                 }
 724         }
 725
 726         /* Add all incident edges to edge bucket, since they are now independent. */
 727         for (edge_index = 0; edge_index < max_degree; ++edge_index) {
 728                 insert_into_edge_bucket(node->edges[edge_index]);
 729         }
 730 }
 731
 732 static pbqp_node *get_node_with_max_degree(void)
 733 {
 734         pbqp_node  **bucket       = node_buckets[3];
 735         unsigned     bucket_len   = node_bucket_get_length(bucket);
 736         unsigned     bucket_index;
 737         unsigned     max_degree   = 0;
 738         pbqp_node   *result       = NULL;
 739
 740         for (bucket_index = 0; bucket_index < bucket_len; ++bucket_index) {
 741                 pbqp_node *candidate = bucket[bucket_index];
 742                 unsigned   degree    = pbqp_node_get_degree(candidate);
 743
 744                 if (degree > max_degree) {
 745                         result = candidate;
 746                         max_degree = degree;
 747                 }
 748         }
 749
 750         return result;
 751 }
 752
 753 static unsigned get_local_minimal_alternative(pbqp *pbqp, pbqp_node *node)
 754 {
 755         pbqp_edge   *edge;
 756         vector      *node_vec;
 757         vector      *vec;
 758         pbqp_matrix *mat;
 759         unsigned     edge_index;
 760         unsigned     max_degree   = 0;
 761         unsigned     node_index;
 762         unsigned     node_len;
 763         unsigned     min_index    = 0;
 764         num          min          = INF_COSTS;
 765         int          is_src;
 766
 767         assert(pbqp);
 768         assert(node);
 769         node_vec = node->costs;
 770         node_len = node_vec->len;
 771
 772         for (node_index = 0; node_index < node_len; ++node_index) {
 773                 num value = node_vec->entries[node_index].data;
 774
 775                 for (edge_index = 0; edge_index < max_degree; ++edge_index) {
 776                         edge   = node->edges[edge_index];
 777                         mat    = edge->costs;
 778                         is_src = edge->src == node;
 779
 780                         if (is_src) {
 781                                 vec = vector_copy(pbqp, edge->tgt->costs);
 782                                 vector_add_matrix_row(vec, mat, node_index);
 783                         } else {
 784                                 vec = vector_copy(pbqp, edge->src->costs);
 785                                 vector_add_matrix_col(vec, mat, node_index);
 786                         }
 787
 788                         value = pbqp_add(value, vector_get_min(vec));
 789
 790                         obstack_free(&pbqp->obstack, vec);
 791                 }
 792
 793                 if (value < min) {
 794                         min = value;
 795                         min_index = node_index;
 796                 }
 797         }
 798
 799         return min_index;
 800 }
 801
 802 void apply_RN(pbqp *pbqp)
 803 {
 804         pbqp_node   *node         = NULL;
 805         unsigned     min_index    = 0;
 806
 807         assert(pbqp);
 808
 809         /* We want to reduce a node with maximum degree. */
 810         node = get_node_with_max_degree();
 811         assert(node);
 812
 813         if (pbqp->dump_file) {
 814                 char     txt[100];
 815                 sprintf(txt, "RN-Reduction of Node n%d", node->index);
 816                 dump_section(pbqp->dump_file, 2, txt);
 817                 pbqp_dump_graph(pbqp);
 818         }
 819
 820         min_index = get_local_minimal_alternative(pbqp, node);
 821
 822         if (pbqp->dump_file) {
 823                 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
 824                                         node->index, min_index);
 825         }
 826
 827         /* Now that we found the local minimum set all other costs to infinity. */
 828         select_alternative(node, min_index);
 829 }
 830
 831 static unsigned get_minimal_alternative(pbqp *pbqp, pbqp_node *node)
 832 {
 833         pbqp_edge   *edge;
 834         vector      *node_vec;
 835         vector      *vec;
 836         pbqp_matrix *mat;
 837         unsigned     edge_index;
 838         unsigned     max_degree   = 0;
 839         unsigned     node_index;
 840         unsigned     node_len;
 841         unsigned     min_index    = 0;
 842         num          min          = INF_COSTS;
 843         int          is_src;
 844
 845         assert(pbqp);
 846         assert(node);
 847         node_vec = node->costs;
 848         node_len = node_vec->len;
 849
 850         for (node_index = 0; node_index < node_len; ++node_index) {
 851                 num value = node_vec->entries[node_index].data;
 852
 853                 /* Some node buckets and the edge bucket should be empty. */
 854                 assert(node_bucket_get_length(node_buckets[1]) == 0);
 855                 assert(node_bucket_get_length(node_buckets[2]) == 0);
 856                 assert(edge_bucket_get_length(edge_bucket)     == 0);
 857
 858                 /* Save current PBQP state. */
 859                 pbqp_node_bucket *bucket_deg0 = node_bucket_deep_copy(node_buckets[0]);
 860                 pbqp_node_bucket *bucket_deg3 = node_bucket_deep_copy(node_buckets[3]);
 861                 pbqp_node_bucket *bucket_red  = node_bucket_deep_copy(reduced_bucket);
 862
 863                 /* TODO */
 864
 865                 if (value < min) {
 866                         min = value;
 867                         min_index = node_index;
 868                 }
 869         }
 870         return 0;
 871 }
 872
 873 void apply_Brute_Force(pbqp *pbqp)
 874 {
 875         pbqp_node   *node         = NULL;
 876         unsigned     min_index    = 0;
 877
 878         assert(pbqp);
 879
 880         /* We want to reduce a node with maximum degree. */
 881         node = get_node_with_max_degree();
 882         assert(node);
 883
 884         if (pbqp->dump_file) {
 885                 char     txt[100];
 886                 sprintf(txt, "BF-Reduction of Node n%d", node->index);
 887                 dump_section(pbqp->dump_file, 2, txt);
 888                 pbqp_dump_graph(pbqp);
 889         }
 890
 891         min_index = get_minimal_alternative(pbqp, node);
 892
 893         if (pbqp->dump_file) {
 894                 fprintf(pbqp->dump_file, "node n%d is set to %d<br><br>\n",
 895                                         node->index, min_index);
 896         }
 897
 898         /* Now that we found the minimum set all other costs to infinity. */
 899         select_alternative(node, min_index);
 900 }
 901
 902 void back_propagate_RI(pbqp *pbqp, pbqp_node *node)
 903 {
 904         pbqp_edge   *edge;
 905         pbqp_node   *other;
 906         pbqp_matrix *mat;
 907         vector      *vec;
 908         int          is_src;
 909
 910         assert(pbqp);
 911         assert(node);
 912
 913         edge = node->edges[0];
 914         mat = edge->costs;
 915         is_src = edge->src == node;
 916         vec = node->costs;
 917
 918         if (is_src) {
 919                 other = edge->tgt;
 920                 assert(other);
 921                 vector_add_matrix_col(vec, mat, other->solution);
 922         } else {
 923                 other = edge->src;
 924                 assert(other);
 925                 vector_add_matrix_row(vec, mat, other->solution);
 926         }
 927
 928         node->solution = vector_get_min_index(vec);
 929         if (pbqp->dump_file) {
 930                 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
 931         }
 932 }
 933
 934 void back_propagate_RII(pbqp *pbqp, pbqp_node *node)
 935 {
 936         pbqp_edge   *src_edge   = node->edges[0];
 937         pbqp_edge   *tgt_edge   = node->edges[1];
 938         int          src_is_src = src_edge->src == node;
 939         int          tgt_is_src = tgt_edge->src == node;
 940         pbqp_matrix *src_mat;
 941         pbqp_matrix *tgt_mat;
 942         pbqp_node   *src_node;
 943         pbqp_node   *tgt_node;
 944         vector      *vec;
 945         vector      *node_vec;
 946         unsigned     col_index;
 947         unsigned     row_index;
 948
 949         assert(pbqp);
 950
 951         if (src_is_src) {
 952                 src_node = src_edge->tgt;
 953         } else {
 954                 src_node = src_edge->src;
 955         }
 956
 957         if (tgt_is_src) {
 958                 tgt_node = tgt_edge->tgt;
 959         } else {
 960                 tgt_node = tgt_edge->src;
 961         }
 962
 963         /* Swap nodes if necessary. */
 964         if (tgt_node->index < src_node->index) {
 965                 pbqp_node *tmp_node;
 966                 pbqp_edge *tmp_edge;
 967
 968                 tmp_node = src_node;
 969                 src_node = tgt_node;
 970                 tgt_node = tmp_node;
 971
 972                 tmp_edge = src_edge;
 973                 src_edge = tgt_edge;
 974                 tgt_edge = tmp_edge;
 975
 976                 src_is_src = src_edge->src == node;
 977                 tgt_is_src = tgt_edge->src == node;
 978         }
 979
 980         src_mat = src_edge->costs;
 981         tgt_mat = tgt_edge->costs;
 982
 983         node_vec = node->costs;
 984
 985         row_index = src_node->solution;
 986         col_index = tgt_node->solution;
 987
 988         vec = vector_copy(pbqp, node_vec);
 989
 990         if (src_is_src) {
 991                 vector_add_matrix_col(vec, src_mat, row_index);
 992         } else {
 993                 vector_add_matrix_row(vec, src_mat, row_index);
 994         }
 995
 996         if (tgt_is_src) {
 997                 vector_add_matrix_col(vec, tgt_mat, col_index);
 998         } else {
 999                 vector_add_matrix_row(vec, tgt_mat, col_index);
1000         }
1001
1002         node->solution = vector_get_min_index(vec);
1003         if (pbqp->dump_file) {
1004                 fprintf(pbqp->dump_file, "node n%d is set to %d<br>\n", node->index, node->solution);
1005         }
1006
1007         obstack_free(&pbqp->obstack, vec);
1008 }
1009
1010 int node_is_reduced(pbqp_node *node)
1011 {
1012         if (!reduced_bucket) return 0;
1013
1014         if (pbqp_node_get_degree(node) == 0) return 1;
1015
1016         return node_bucket_contains(reduced_bucket, node);
1017 }