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