hungarian.c 10.9 KB
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 Christian Würdig committed Sep 13, 2006 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ``````/******************************************************************** ******************************************************************** ** ** libhungarian by Cyrill Stachniss, 2004 ** ** Added and adapted to libFirm by Christian Wuerdig, 2006 ** ** Solving the Minimum Assignment Problem using the ** Hungarian Method. ** ** ** This file may be freely copied and distributed! ** ** ** Parts of the used code was originally provided by the ** "Stanford GraphGase", but I made changes to this code. ** As asked by the copyright node of the "Stanford GraphGase", ** I hereby proclaim that this file are *NOT* part of the ** "Stanford GraphGase" distrubition! ** ** This file is distributed in the hope that it will be useful, ** but WITHOUT ANY WARRANTY; without even the implied ** warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR ** PURPOSE. ** ******************************************************************** ********************************************************************/ `````` 27 28 29 30 31 ``````/** * @file * @brief Solving the Minimum Assignment Problem using the Hungarian Method. * @version \$Id\$ */ `````` Matthias Braun committed Dec 10, 2006 32 33 34 35 ``````#ifdef HAVE_CONFIG_H # include "config.h" #endif `````` Christian Würdig committed Sep 13, 2006 36 37 38 39 40 41 42 43 ``````#include #include #include #include "irtools.h" #include "xmalloc.h" #include "debug.h" #include "obst.h" `````` Christian Würdig committed Sep 13, 2006 44 ``````#include "bitset.h" `````` Christian Würdig committed Sep 13, 2006 45 46 47 48 49 50 `````` #include "hungarian.h" #define INF (0x7FFFFFFF) struct _hungarian_problem_t { `````` Christian Würdig committed Sep 13, 2006 51 52 53 54 55 56 57 58 `````` int num_rows; /**< number of rows */ int num_cols; /**< number of columns */ int **cost; /**< the cost matrix */ int width; /**< the width for cost matrix dumper */ int max_cost; /**< the maximal costs in the matrix */ int match_type; /**< PERFECT or NORMAL matching */ bitset_t *missing_left; /**< left side nodes having no edge to the right side */ bitset_t *missing_right; /**< right side nodes having no edge to the left side */ `````` Christian Würdig committed Sep 13, 2006 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 `````` struct obstack obst; DEBUG_ONLY(firm_dbg_module_t *dbg); }; static INLINE void *get_init_mem(struct obstack *obst, long sz) { void *p = obstack_alloc(obst, sz); memset(p, 0, sz); return p; } static void hungarian_dump_f(FILE *f, int **C, int rows, int cols, int width) { int i, j; fprintf(f , "\n"); for (i = 0; i < rows; i++) { fprintf(f, " ["); for (j = 0; j < cols; j++) { fprintf(f, "%*d", width, C[i][j]); } fprintf(f, "]\n"); } fprintf(f, "\n"); } void hungarian_print_costmatrix(hungarian_problem_t *p) { hungarian_dump_f(stderr, p->cost, p->num_rows, p->num_cols, p->width); } /** * Create the object and allocate memory for the data structures. */ `````` Christian Würdig committed Sep 13, 2006 90 ``````hungarian_problem_t *hungarian_new(int rows, int cols, int width, int match_type) { `````` Christian Würdig committed Sep 13, 2006 91 92 93 `````` int i; hungarian_problem_t *p = xmalloc(sizeof(*p)); `````` Matthias Braun committed Jan 29, 2007 94 `````` memset(p, 0, sizeof(p[0])); `````` Christian Würdig committed Sep 13, 2006 95 96 97 98 99 100 101 102 103 104 105 106 `````` FIRM_DBG_REGISTER(p->dbg, "firm.hungarian"); /* Is the number of cols not equal to number of rows ? If yes, expand with 0 - cols / 0 - cols */ rows = MAX(cols, rows); cols = rows; obstack_init(&p->obst); `````` Christian Würdig committed Sep 13, 2006 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 `````` p->num_rows = rows; p->num_cols = cols; p->width = width; p->match_type = match_type; /* In case of normal matching, we have to keep track of nodes without edges to kill them in the assignment later. */ if (match_type == HUNGARIAN_MATCH_NORMAL) { p->missing_left = bitset_obstack_alloc(&p->obst, rows); p->missing_right = bitset_obstack_alloc(&p->obst, cols); bitset_set_all(p->missing_left); bitset_set_all(p->missing_right); } `````` Christian Würdig committed Sep 13, 2006 123 124 `````` /* allocate space for cost matrix */ `````` Christian Würdig committed Sep 13, 2006 125 `````` p->cost = (int **)get_init_mem(&p->obst, rows * sizeof(p->cost[0])); `````` Christian Würdig committed Sep 13, 2006 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 `````` for (i = 0; i < p->num_rows; i++) p->cost[i] = (int *)get_init_mem(&p->obst, cols * sizeof(p->cost[0][0])); return p; } /** * Prepare the cost matrix. */ void hungarian_prepare_cost_matrix(hungarian_problem_t *p, int mode) { int i, j; if (mode == HUNGARIAN_MODE_MAXIMIZE_UTIL) { for (i = 0; i < p->num_rows; i++) { for (j = 0; j < p->num_cols; j++) { p->cost[i][j] = p->max_cost - p->cost[i][j]; } } } else if (mode == HUNGARIAN_MODE_MINIMIZE_COST) { /* nothing to do */ } else fprintf(stderr, "Unknown mode. Mode was set to HUNGARIAN_MODE_MINIMIZE_COST.\n"); } /** * Set cost[left][right] to cost. */ void hungarian_add(hungarian_problem_t *p, int left, int right, int cost) { assert(p->num_rows > left && "Invalid row selected."); assert(p->num_cols > right && "Invalid column selected."); `````` Matthias Braun committed Jan 29, 2007 158 `````` assert(cost >= 0); `````` Christian Würdig committed Sep 13, 2006 159 160 161 `````` p->cost[left][right] = cost; p->max_cost = MAX(p->max_cost, cost); `````` Christian Würdig committed Sep 13, 2006 162 163 164 165 166 `````` if (p->match_type == HUNGARIAN_MATCH_NORMAL) { bitset_clear(p->missing_left, left); bitset_clear(p->missing_right, right); } `````` Christian Würdig committed Sep 13, 2006 167 168 169 170 171 172 173 174 175 176 ``````} /** * Set cost[left][right] to 0. */ void hungarian_remv(hungarian_problem_t *p, int left, int right) { assert(p->num_rows > left && "Invalid row selected."); assert(p->num_cols > right && "Invalid column selected."); p->cost[left][right] = 0; `````` Christian Würdig committed Sep 13, 2006 177 178 179 180 181 `````` if (p->match_type == HUNGARIAN_MATCH_NORMAL) { bitset_set(p->missing_left, left); bitset_set(p->missing_right, right); } `````` Christian Würdig committed Sep 13, 2006 182 183 184 185 186 187 188 189 190 191 192 193 194 ``````} /** * Frees all allocated memory. */ void hungarian_free(hungarian_problem_t* p) { obstack_free(&p->obst, NULL); xfree(p); } /** * Do the assignment. */ `````` Christian Würdig committed Sep 25, 2006 195 ``````int hungarian_solve(hungarian_problem_t* p, int *assignment, int *final_cost, int cost_threshold) { `````` Christian Würdig committed Sep 13, 2006 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 `````` int i, j, m, n, k, l, s, t, q, unmatched, cost; int *col_mate; int *row_mate; int *parent_row; int *unchosen_row; int *row_dec; int *col_inc; int *slack; int *slack_row; cost = 0; m = p->num_rows; n = p->num_cols; col_mate = xcalloc(p->num_rows, sizeof(col_mate[0])); unchosen_row = xcalloc(p->num_rows, sizeof(unchosen_row[0])); row_dec = xcalloc(p->num_rows, sizeof(row_dec[0])); slack_row = xcalloc(p->num_rows, sizeof(slack_row[0])); row_mate = xcalloc(p->num_cols, sizeof(row_mate[0])); parent_row = xcalloc(p->num_cols, sizeof(parent_row[0])); col_inc = xcalloc(p->num_cols, sizeof(col_inc[0])); slack = xcalloc(p->num_cols, sizeof(slack[0])); memset(assignment, -1, m * sizeof(assignment[0])); /* Begin subtract column minima in order to start with lots of zeros 12 */ DBG((p->dbg, LEVEL_1, "Using heuristic\n")); for (l = 0; l < n; ++l) { s = p->cost[0][l]; for (k = 1; k < m; ++k) { if (p->cost[k][l] < s) s = p->cost[k][l]; } cost += s; if (s != 0) { for (k = 0; k < m; ++k) p->cost[k][l] -= s; } } /* End subtract column minima in order to start with lots of zeros 12 */ /* Begin initial state 16 */ t = 0; for (l = 0; l < n; ++l) { row_mate[l] = -1; parent_row[l] = -1; col_inc[l] = 0; slack[l] = INF; } for (k = 0; k < m; ++k) { s = p->cost[k][0]; for (l = 1; l < n; ++l) { if (p->cost[k][l] < s) s = p->cost[k][l]; } row_dec[k] = s; for (l = 0; l < n; ++l) { if (s == p->cost[k][l] && row_mate[l] < 0) { col_mate[k] = l; row_mate[l] = k; DBG((p->dbg, LEVEL_1, "matching col %d == row %d\n", l, k)); goto row_done; } } col_mate[k] = -1; DBG((p->dbg, LEVEL_1, "node %d: unmatched row %d\n", t, k)); unchosen_row[t++] = k; row_done: ; } /* End initial state 16 */ /* Begin Hungarian algorithm 18 */ if (t == 0) goto done; unmatched = t; while (1) { DBG((p->dbg, LEVEL_1, "Matched %d rows.\n", m - t)); q = 0; while (1) { while (q < t) { /* Begin explore node q of the forest 19 */ k = unchosen_row[q]; s = row_dec[k]; for (l = 0; l < n; ++l) { if (slack[l]) { int del = p->cost[k][l] - s + col_inc[l]; if (del < slack[l]) { if (del == 0) { if (row_mate[l] < 0) goto breakthru; slack[l] = 0; parent_row[l] = k; DBG((p->dbg, LEVEL_1, "node %d: row %d == col %d -- row %d\n", t, row_mate[l], l, k)); unchosen_row[t++] = row_mate[l]; } else { slack[l] = del; slack_row[l] = k; } } } } /* End explore node q of the forest 19 */ q++; } /* Begin introduce a new zero into the matrix 21 */ s = INF; for (l = 0; l < n; ++l) { if (slack[l] && slack[l] < s) s = slack[l]; } for (q = 0; q < t; ++q) row_dec[unchosen_row[q]] += s; for (l = 0; l < n; ++l) { if (slack[l]) { slack[l] -= s; if (slack[l] == 0) { /* Begin look at a new zero 22 */ k = slack_row[l]; DBG((p->dbg, LEVEL_1, "Decreasing uncovered elements by %d produces zero at [%d, %d]\n", s, k, l)); if (row_mate[l] < 0) { for (j = l + 1; j < n; ++j) { if (slack[j] == 0) col_inc[j] += s; } goto breakthru; } else { parent_row[l] = k; DBG((p->dbg, LEVEL_1, "node %d: row %d == col %d -- row %d\n", t, row_mate[l], l, k)); unchosen_row[t++] = row_mate[l]; } /* End look at a new zero 22 */ } } else { col_inc[l] += s; } } /* End introduce a new zero into the matrix 21 */ } breakthru: /* Begin update the matching 20 */ DBG((p->dbg, LEVEL_1, "Breakthrough at node %d of %d.\n", q, t)); while (1) { j = col_mate[k]; col_mate[k] = l; row_mate[l] = k; DBG((p->dbg, LEVEL_1, "rematching col %d == row %d\n", l, k)); if (j < 0) break; k = parent_row[j]; l = j; } /* End update the matching 20 */ if (--unmatched == 0) goto done; /* Begin get ready for another stage 17 */ t = 0; for (l = 0; l < n; ++l) { parent_row[l] = -1; slack[l] = INF; } for (k = 0; k < m; ++k) { if (col_mate[k] < 0) { DBG((p->dbg, LEVEL_1, "node %d: unmatched row %d\n", t, k)); unchosen_row[t++] = k; } } /* End get ready for another stage 17 */ } done: /* Begin double check the solution 23 */ for (k = 0; k < m; ++k) { for (l = 0; l < n; ++l) { if (p->cost[k][l] < row_dec[k] - col_inc[l]) return -1; } } for (k = 0; k < m; ++k) { l = col_mate[k]; if (l < 0 || p->cost[k][l] != row_dec[k] - col_inc[l]) return -2; } for (k = l = 0; l < n; ++l) { if (col_inc[l]) k++; } if (k > m) return -3; /* End double check the solution 23 */ /* End Hungarian algorithm 18 */ /* collect the assigned values */ for (i = 0; i < m; ++i) { `````` Christian Würdig committed Sep 25, 2006 419 420 421 422 `````` if (cost_threshold > 0 && p->cost[i][col_mate[i]] >= cost_threshold) assignment[i] = -1; /* remove matching having cost > threshold */ else assignment[i] = col_mate[i]; `````` Christian Würdig committed Sep 13, 2006 423 424 `````` } `````` Christian Würdig committed Sep 13, 2006 425 426 427 428 429 430 431 432 `````` /* In case of normal matching: remove impossible ones */ if (p->match_type == HUNGARIAN_MATCH_NORMAL) { for (i = 0; i < m; ++i) { if (bitset_is_set(p->missing_left, i) || bitset_is_set(p->missing_right, col_mate[i])) assignment[i] = -1; } } `````` Christian Würdig committed Sep 13, 2006 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 `````` for (k = 0; k < m; ++k) { for (l = 0; l < n; ++l) { p->cost[k][l] = p->cost[k][l] - row_dec[k] + col_inc[l]; } } for (i = 0; i < m; ++i) cost += row_dec[i]; for (i = 0; i < n; ++i) cost -= col_inc[i]; DBG((p->dbg, LEVEL_1, "Cost is %d\n", cost)); xfree(slack); xfree(col_inc); xfree(parent_row); xfree(row_mate); xfree(slack_row); xfree(row_dec); xfree(unchosen_row); xfree(col_mate); `````` 456 457 458 `````` *final_cost = cost; return 0; `````` Christian Würdig committed Sep 13, 2006 459 ``}``