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      width;             /**< the width for cost matrix dumper */
  53         int      max_cost;          /**< the maximal costs in the matrix */
  54         int      match_type;        /**< PERFECT or NORMAL matching */
  55         bitset_t *missing_left;     /**< left side nodes having no edge to the right side */
  56         bitset_t *missing_right;    /**< right side nodes having no edge to the left side */
  57         struct obstack obst;
  58         DEBUG_ONLY(firm_dbg_module_t *dbg);
  59 };
  60
  61 static inline void *get_init_mem(struct obstack *obst, long sz) {
  62         void *p = obstack_alloc(obst, sz);
  63         memset(p, 0, sz);
  64         return p;
  65 }
  66
  67 static void hungarian_dump_f(FILE *f, int **C, int rows, int cols, int width) {
  68         int i, j;
  69
  70         fprintf(f , "\n");
  71         for (i = 0; i < rows; i++) {
  72                 fprintf(f, " [");
  73                 for (j = 0; j < cols; j++) {
  74                         fprintf(f, "%*d", width, C[i][j]);
  75                 }
  76                 fprintf(f, "]\n");
  77         }
  78         fprintf(f, "\n");
  79 }
  80
  81 void hungarian_print_costmatrix(hungarian_problem_t *p) {
  82         hungarian_dump_f(stderr, p->cost, p->num_rows, p->num_cols, p->width);
  83 }
  84
  85 /**
  86  * Create the object and allocate memory for the data structures.
  87  */
  88 hungarian_problem_t *hungarian_new(int rows, int cols, int width, int match_type) {
  89         int i;
  90         hungarian_problem_t *p = XMALLOCZ(hungarian_problem_t);
  91
  92         FIRM_DBG_REGISTER(p->dbg, "firm.hungarian");
  93
  94         /*
  95                 Is the number of cols  not equal to number of rows ?
  96                 If yes, expand with 0 - cols / 0 - cols
  97         */
  98         rows = MAX(cols, rows);
  99         cols = rows;
 100
 101         obstack_init(&p->obst);
 102
 103         p->num_rows   = rows;
 104         p->num_cols   = cols;
 105         p->width      = width;
 106         p->match_type = match_type;
 107
 108         /*
 109                 In case of normal matching, we have to keep
 110                 track of nodes without edges to kill them in
 111                 the assignment later.
 112         */
 113         if (match_type == HUNGARIAN_MATCH_NORMAL) {
 114                 p->missing_left  = bitset_obstack_alloc(&p->obst, rows);
 115                 p->missing_right = bitset_obstack_alloc(&p->obst, cols);
 116                 bitset_set_all(p->missing_left);
 117                 bitset_set_all(p->missing_right);
 118         }
 119
 120         /* allocate space for cost matrix */
 121         p->cost = (int **)get_init_mem(&p->obst, rows * sizeof(p->cost[0]));
 122         for (i = 0; i < p->num_rows; i++)
 123                 p->cost[i] = (int *)get_init_mem(&p->obst, cols * sizeof(p->cost[0][0]));
 124
 125         return p;
 126 }
 127
 128 /**
 129  * Prepare the cost matrix.
 130  */
 131 void hungarian_prepare_cost_matrix(hungarian_problem_t *p, int mode) {
 132         int i, j;
 133
 134         if (mode == HUNGARIAN_MODE_MAXIMIZE_UTIL) {
 135                 for (i = 0; i < p->num_rows; i++) {
 136                         for (j = 0; j < p->num_cols; j++) {
 137                                 p->cost[i][j] = p->max_cost - p->cost[i][j];
 138                         }
 139                 }
 140         }
 141         else if (mode == HUNGARIAN_MODE_MINIMIZE_COST) {
 142                 /* nothing to do */
 143         }
 144         else
 145                 fprintf(stderr, "Unknown mode. Mode was set to HUNGARIAN_MODE_MINIMIZE_COST.\n");
 146 }
 147
 148 /**
 149  * Set cost[left][right] to cost.
 150  */
 151 void hungarian_add(hungarian_problem_t *p, int left, int right, int cost) {
 152         assert(p->num_rows > left  && "Invalid row selected.");
 153         assert(p->num_cols > right && "Invalid column selected.");
 154         assert(cost >= 0);
 155
 156         p->cost[left][right] = cost;
 157         p->max_cost          = MAX(p->max_cost, cost);
 158
 159         if (p->match_type == HUNGARIAN_MATCH_NORMAL) {
 160                 bitset_clear(p->missing_left, left);
 161                 bitset_clear(p->missing_right, right);
 162         }
 163 }
 164
 165 /**
 166  * Set cost[left][right] to 0.
 167  */
 168 void hungarian_remv(hungarian_problem_t *p, int left, int right) {
 169         assert(p->num_rows > left  && "Invalid row selected.");
 170         assert(p->num_cols > right && "Invalid column selected.");
 171
 172         p->cost[left][right] = 0;
 173
 174         if (p->match_type == HUNGARIAN_MATCH_NORMAL) {
 175                 bitset_set(p->missing_left, left);
 176                 bitset_set(p->missing_right, right);
 177         }
 178 }
 179
 180 /**
 181  * Frees all allocated memory.
 182  */
 183 void hungarian_free(hungarian_problem_t* p) {
 184         obstack_free(&p->obst, NULL);
 185         xfree(p);
 186 }
 187
 188 /**
 189  * Do the assignment.
 190  */
 191 int hungarian_solve(hungarian_problem_t* p, int *assignment, int *final_cost, int cost_threshold) {
 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         while (1) {
 279                 DBG((p->dbg, LEVEL_1, "Matched %d rows.\n", m - t));
 280                 q = 0;
 281
 282                 while (1) {
 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                 while (1) {
 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         *final_cost = cost;
 453
 454         return 0;
 455 }