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