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