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) {
85 hungarian_problem_t *p = xmalloc(sizeof(*p));
87 memset(p, 0, sizeof(p));
89 FIRM_DBG_REGISTER(p->dbg, "firm.hungarian");
92 Is the number of cols not equal to number of rows ?
93 If yes, expand with 0 - cols / 0 - cols
95 rows = MAX(cols, rows);
98 obstack_init(&p->obst);
103 p->match_type = match_type;
106 In case of normal matching, we have to keep
107 track of nodes without edges to kill them in
108 the assignment later.
110 if (match_type == HUNGARIAN_MATCH_NORMAL) {
111 p->missing_left = bitset_obstack_alloc(&p->obst, rows);
112 p->missing_right = bitset_obstack_alloc(&p->obst, cols);
113 bitset_set_all(p->missing_left);
114 bitset_set_all(p->missing_right);
117 /* allocate space for cost matrix */
118 p->cost = (int **)get_init_mem(&p->obst, rows * sizeof(p->cost[0]));
119 for (i = 0; i < p->num_rows; i++)
120 p->cost[i] = (int *)get_init_mem(&p->obst, cols * sizeof(p->cost[0][0]));
126 * Prepare the cost matrix.
128 void hungarian_prepare_cost_matrix(hungarian_problem_t *p, int mode) {
131 if (mode == HUNGARIAN_MODE_MAXIMIZE_UTIL) {
132 for (i = 0; i < p->num_rows; i++) {
133 for (j = 0; j < p->num_cols; j++) {
134 p->cost[i][j] = p->max_cost - p->cost[i][j];
138 else if (mode == HUNGARIAN_MODE_MINIMIZE_COST) {
142 fprintf(stderr, "Unknown mode. Mode was set to HUNGARIAN_MODE_MINIMIZE_COST.\n");
146 * Set cost[left][right] to cost.
148 void hungarian_add(hungarian_problem_t *p, int left, int right, int cost) {
149 assert(p->num_rows > left && "Invalid row selected.");
150 assert(p->num_cols > right && "Invalid column selected.");
152 p->cost[left][right] = cost;
153 p->max_cost = MAX(p->max_cost, cost);
155 if (p->match_type == HUNGARIAN_MATCH_NORMAL) {
156 bitset_clear(p->missing_left, left);
157 bitset_clear(p->missing_right, right);
162 * Set cost[left][right] to 0.
164 void hungarian_remv(hungarian_problem_t *p, int left, int right) {
165 assert(p->num_rows > left && "Invalid row selected.");
166 assert(p->num_cols > right && "Invalid column selected.");
168 p->cost[left][right] = 0;
170 if (p->match_type == HUNGARIAN_MATCH_NORMAL) {
171 bitset_set(p->missing_left, left);
172 bitset_set(p->missing_right, right);
177 * Frees all allocated memory.
179 void hungarian_free(hungarian_problem_t* p) {
180 obstack_free(&p->obst, NULL);
187 int hungarian_solve(hungarian_problem_t* p, int *assignment, int *final_cost) {
188 int i, j, m, n, k, l, s, t, q, unmatched, cost;
202 col_mate = xcalloc(p->num_rows, sizeof(col_mate[0]));
203 unchosen_row = xcalloc(p->num_rows, sizeof(unchosen_row[0]));
204 row_dec = xcalloc(p->num_rows, sizeof(row_dec[0]));
205 slack_row = xcalloc(p->num_rows, sizeof(slack_row[0]));
207 row_mate = xcalloc(p->num_cols, sizeof(row_mate[0]));
208 parent_row = xcalloc(p->num_cols, sizeof(parent_row[0]));
209 col_inc = xcalloc(p->num_cols, sizeof(col_inc[0]));
210 slack = xcalloc(p->num_cols, sizeof(slack[0]));
212 memset(assignment, -1, m * sizeof(assignment[0]));
214 /* Begin subtract column minima in order to start with lots of zeros 12 */
215 DBG((p->dbg, LEVEL_1, "Using heuristic\n"));
217 for (l = 0; l < n; ++l) {
220 for (k = 1; k < m; ++k) {
221 if (p->cost[k][l] < s)
228 for (k = 0; k < m; ++k)
232 /* End subtract column minima in order to start with lots of zeros 12 */
234 /* Begin initial state 16 */
236 for (l = 0; l < n; ++l) {
243 for (k = 0; k < m; ++k) {
246 for (l = 1; l < n; ++l) {
247 if (p->cost[k][l] < s)
253 for (l = 0; l < n; ++l) {
254 if (s == p->cost[k][l] && row_mate[l] < 0) {
257 DBG((p->dbg, LEVEL_1, "matching col %d == row %d\n", l, k));
263 DBG((p->dbg, LEVEL_1, "node %d: unmatched row %d\n", t, k));
264 unchosen_row[t++] = k;
267 /* End initial state 16 */
269 /* Begin Hungarian algorithm 18 */
275 DBG((p->dbg, LEVEL_1, "Matched %d rows.\n", m - t));
280 /* Begin explore node q of the forest 19 */
284 for (l = 0; l < n; ++l) {
286 int del = p->cost[k][l] - s + col_inc[l];
288 if (del < slack[l]) {
295 DBG((p->dbg, LEVEL_1, "node %d: row %d == col %d -- row %d\n", t, row_mate[l], l, k));
296 unchosen_row[t++] = row_mate[l];
305 /* End explore node q of the forest 19 */
309 /* Begin introduce a new zero into the matrix 21 */
311 for (l = 0; l < n; ++l) {
312 if (slack[l] && slack[l] < s)
316 for (q = 0; q < t; ++q)
317 row_dec[unchosen_row[q]] += s;
319 for (l = 0; l < n; ++l) {
323 /* Begin look at a new zero 22 */
325 DBG((p->dbg, LEVEL_1, "Decreasing uncovered elements by %d produces zero at [%d, %d]\n", s, k, l));
326 if (row_mate[l] < 0) {
327 for (j = l + 1; j < n; ++j) {
335 DBG((p->dbg, LEVEL_1, "node %d: row %d == col %d -- row %d\n", t, row_mate[l], l, k));
336 unchosen_row[t++] = row_mate[l];
338 /* End look at a new zero 22 */
345 /* End introduce a new zero into the matrix 21 */
348 /* Begin update the matching 20 */
349 DBG((p->dbg, LEVEL_1, "Breakthrough at node %d of %d.\n", q, t));
355 DBG((p->dbg, LEVEL_1, "rematching col %d == row %d\n", l, k));
362 /* End update the matching 20 */
364 if (--unmatched == 0)
367 /* Begin get ready for another stage 17 */
369 for (l = 0; l < n; ++l) {
374 for (k = 0; k < m; ++k) {
375 if (col_mate[k] < 0) {
376 DBG((p->dbg, LEVEL_1, "node %d: unmatched row %d\n", t, k));
377 unchosen_row[t++] = k;
380 /* End get ready for another stage 17 */
384 /* Begin double check the solution 23 */
385 for (k = 0; k < m; ++k) {
386 for (l = 0; l < n; ++l) {
387 if (p->cost[k][l] < row_dec[k] - col_inc[l])
392 for (k = 0; k < m; ++k) {
394 if (l < 0 || p->cost[k][l] != row_dec[k] - col_inc[l])
398 for (k = l = 0; l < n; ++l) {
405 /* End double check the solution 23 */
407 /* End Hungarian algorithm 18 */
409 /* collect the assigned values */
410 for (i = 0; i < m; ++i) {
411 assignment[i] = col_mate[i];
414 /* In case of normal matching: remove impossible ones */
415 if (p->match_type == HUNGARIAN_MATCH_NORMAL) {
416 for (i = 0; i < m; ++i) {
417 if (bitset_is_set(p->missing_left, i) || bitset_is_set(p->missing_right, col_mate[i]))
422 for (k = 0; k < m; ++k) {
423 for (l = 0; l < n; ++l) {
424 p->cost[k][l] = p->cost[k][l] - row_dec[k] + col_inc[l];
428 for (i = 0; i < m; ++i)
431 for (i = 0; i < n; ++i)
434 DBG((p->dbg, LEVEL_1, "Cost is %d\n", cost));