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