hungarian.c 10.6 KB
 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 Oct 11, 2008 32 ``````#include "config.h" `````` Matthias Braun committed Dec 10, 2006 33 `````` `````` Christian Würdig committed Sep 13, 2006 34 35 36 37 38 39 40 41 ``````#include #include #include #include "irtools.h" #include "xmalloc.h" #include "debug.h" #include "obst.h" `````` Christian Würdig committed Sep 13, 2006 42 ``````#include "bitset.h" `````` Christian Würdig committed Sep 13, 2006 43 44 45 46 47 48 `````` #include "hungarian.h" #define INF (0x7FFFFFFF) struct _hungarian_problem_t { `````` Christian Würdig committed Sep 13, 2006 49 50 51 52 53 54 55 `````` int num_rows; /**< number of rows */ int num_cols; /**< number of columns */ int **cost; /**< the cost matrix */ 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 56 57 58 59 `````` struct obstack obst; DEBUG_ONLY(firm_dbg_module_t *dbg); }; `````` Matthias Braun committed Mar 02, 2009 60 ``````static inline void *get_init_mem(struct obstack *obst, size_t sz) { `````` Christian Würdig committed Sep 13, 2006 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 `````` 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"); } `````` Matthias Braun committed Mar 02, 2009 80 81 ``````void hungarian_print_costmatrix(hungarian_problem_t *p, int width) { hungarian_dump_f(stderr, p->cost, p->num_rows, p->num_cols, width); `````` Christian Würdig committed Sep 13, 2006 82 83 84 85 86 ``````} /** * Create the object and allocate memory for the data structures. */ `````` Matthias Braun committed Mar 02, 2009 87 ``````hungarian_problem_t *hungarian_new(int rows, int cols, int match_type) { `````` Christian Würdig committed Sep 13, 2006 88 `````` int i; `````` 89 `````` hungarian_problem_t *p = XMALLOCZ(hungarian_problem_t); `````` Christian Würdig committed Sep 13, 2006 90 91 92 93 94 95 96 97 98 99 100 101 `````` 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 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 `````` p->num_rows = rows; p->num_cols = cols; 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 117 118 `````` /* allocate space for cost matrix */ `````` Christian Würdig committed Sep 13, 2006 119 `````` p->cost = (int **)get_init_mem(&p->obst, rows * sizeof(p->cost[0])); `````` Christian Würdig committed Sep 13, 2006 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 `````` 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 152 `````` assert(cost >= 0); `````` Christian Würdig committed Sep 13, 2006 153 154 155 `````` p->cost[left][right] = cost; p->max_cost = MAX(p->max_cost, cost); `````` Christian Würdig committed Sep 13, 2006 156 157 158 159 160 `````` 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 161 162 163 164 165 166 167 168 169 170 ``````} /** * 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 171 172 173 174 175 `````` 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 176 177 178 179 180 181 182 183 184 185 186 187 188 ``````} /** * 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 189 ``````int hungarian_solve(hungarian_problem_t* p, int *assignment, int *final_cost, int cost_threshold) { `````` Christian Würdig committed Sep 13, 2006 190 191 192 193 194 195 196 197 198 199 200 201 202 203 `````` 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; `````` 204 205 206 207 `````` col_mate = XMALLOCNZ(int, p->num_rows); unchosen_row = XMALLOCNZ(int, p->num_rows); row_dec = XMALLOCNZ(int, p->num_rows); slack_row = XMALLOCNZ(int, p->num_rows); `````` Christian Würdig committed Sep 13, 2006 208 `````` `````` 209 210 211 212 `````` row_mate = XMALLOCNZ(int, p->num_cols); parent_row = XMALLOCNZ(int, p->num_cols); col_inc = XMALLOCNZ(int, p->num_cols); slack = XMALLOCNZ(int, p->num_cols); `````` Christian Würdig committed Sep 13, 2006 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 `````` 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 413 414 415 416 `````` 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 417 418 `````` } `````` Christian Würdig committed Sep 13, 2006 419 420 421 422 423 424 425 426 `````` /* 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 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 `````` 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); `````` 450 451 452 `````` *final_cost = cost; return 0; `````` Christian Würdig committed Sep 13, 2006 453 ``}``