1 /********************************************************************
2 ********************************************************************
4 ** libhungarian by Cyrill Stachniss, 2004
6 ** Added and adapted to libFirm by Christian Wuerdig, 2006
8 ** Solving the Minimum Assignment Problem using the
11 ** ** This file may be freely copied and distributed! **
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!
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
24 ********************************************************************
25 ********************************************************************/
39 #include "hungarian.h"
41 #define INF (0x7FFFFFFF)
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 */
53 DEBUG_ONLY(firm_dbg_module_t *dbg);
56 static INLINE void *get_init_mem(struct obstack *obst, long sz) {
57 void *p = obstack_alloc(obst, sz);
62 static void hungarian_dump_f(FILE *f, int **C, int rows, int cols, int width) {
66 for (i = 0; i < rows; i++) {
68 for (j = 0; j < cols; j++) {
69 fprintf(f, "%*d", width, C[i][j]);
76 void hungarian_print_costmatrix(hungarian_problem_t *p) {
77 hungarian_dump_f(stderr, p->cost, p->num_rows, p->num_cols, p->width);
81 * Create the object and allocate memory for the data structures.
83 hungarian_problem_t *hungarian_new(int rows, int cols, int width, int match_type) {
86 hungarian_problem_t *p = xmalloc(sizeof(*p));
88 memset(p, 0, sizeof(p));
90 FIRM_DBG_REGISTER(p->dbg, "firm.hungarian");
93 Is the number of cols not equal to number of rows ?
94 If yes, expand with 0 - cols / 0 - cols
96 rows = MAX(cols, rows);
99 obstack_init(&p->obst);
104 p->match_type = match_type;
107 In case of normal matching, we have to keep
108 track of nodes without edges to kill them in
109 the assignment later.
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);
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]));
127 * Prepare the cost matrix.
129 void hungarian_prepare_cost_matrix(hungarian_problem_t *p, int mode) {
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];
139 else if (mode == HUNGARIAN_MODE_MINIMIZE_COST) {
143 fprintf(stderr, "Unknown mode. Mode was set to HUNGARIAN_MODE_MINIMIZE_COST.\n");
147 * Set cost[left][right] to cost.
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.");
153 p->cost[left][right] = cost;
154 p->max_cost = MAX(p->max_cost, cost);
156 if (p->match_type == HUNGARIAN_MATCH_NORMAL) {
157 bitset_clear(p->missing_left, left);
158 bitset_clear(p->missing_right, right);
163 * Set cost[left][right] to 0.
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.");
169 p->cost[left][right] = 0;
171 if (p->match_type == HUNGARIAN_MATCH_NORMAL) {
172 bitset_set(p->missing_left, left);
173 bitset_set(p->missing_right, right);
178 * Frees all allocated memory.
180 void hungarian_free(hungarian_problem_t* p) {
181 obstack_free(&p->obst, NULL);
188 int hungarian_solve(hungarian_problem_t* p, int *assignment) {
189 int i, j, m, n, k, l, s, t, q, unmatched, cost;
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]));
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]));
213 memset(assignment, -1, m * sizeof(assignment[0]));
215 /* Begin subtract column minima in order to start with lots of zeros 12 */
216 DBG((p->dbg, LEVEL_1, "Using heuristic\n"));
218 for (l = 0; l < n; ++l) {
221 for (k = 1; k < m; ++k) {
222 if (p->cost[k][l] < s)
229 for (k = 0; k < m; ++k)
233 /* End subtract column minima in order to start with lots of zeros 12 */
235 /* Begin initial state 16 */
237 for (l = 0; l < n; ++l) {
244 for (k = 0; k < m; ++k) {
247 for (l = 1; l < n; ++l) {
248 if (p->cost[k][l] < s)
254 for (l = 0; l < n; ++l) {
255 if (s == p->cost[k][l] && row_mate[l] < 0) {
258 DBG((p->dbg, LEVEL_1, "matching col %d == row %d\n", l, k));
264 DBG((p->dbg, LEVEL_1, "node %d: unmatched row %d\n", t, k));
265 unchosen_row[t++] = k;
268 /* End initial state 16 */
270 /* Begin Hungarian algorithm 18 */
276 DBG((p->dbg, LEVEL_1, "Matched %d rows.\n", m - t));
281 /* Begin explore node q of the forest 19 */
285 for (l = 0; l < n; ++l) {
287 int del = p->cost[k][l] - s + col_inc[l];
289 if (del < slack[l]) {
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];
306 /* End explore node q of the forest 19 */
310 /* Begin introduce a new zero into the matrix 21 */
312 for (l = 0; l < n; ++l) {
313 if (slack[l] && slack[l] < s)
317 for (q = 0; q < t; ++q)
318 row_dec[unchosen_row[q]] += s;
320 for (l = 0; l < n; ++l) {
324 /* Begin look at a new zero 22 */
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) {
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];
339 /* End look at a new zero 22 */
346 /* End introduce a new zero into the matrix 21 */
349 /* Begin update the matching 20 */
350 DBG((p->dbg, LEVEL_1, "Breakthrough at node %d of %d.\n", q, t));
356 DBG((p->dbg, LEVEL_1, "rematching col %d == row %d\n", l, k));
363 /* End update the matching 20 */
365 if (--unmatched == 0)
368 /* Begin get ready for another stage 17 */
370 for (l = 0; l < n; ++l) {
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;
381 /* End get ready for another stage 17 */
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])
393 for (k = 0; k < m; ++k) {
395 if (l < 0 || p->cost[k][l] != row_dec[k] - col_inc[l])
399 for (k = l = 0; l < n; ++l) {
406 /* End double check the solution 23 */
408 /* End Hungarian algorithm 18 */
410 /* collect the assigned values */
411 for (i = 0; i < m; ++i) {
412 assignment[i] = col_mate[i];
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]))
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];
429 for (i = 0; i < m; ++i)
432 for (i = 0; i < n; ++i)
435 DBG((p->dbg, LEVEL_1, "Cost is %d\n", cost));