nsz Git - libfirm/blob - ir/adt/hungarian.c

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