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