diff options
| -rw-r--r-- | Makefile | 1 | ||||
| -rw-r--r-- | linear-assignment.c | 201 | ||||
| -rw-r--r-- | linear-assignment.h | 22 |
3 files changed, 224 insertions, 0 deletions
@@ -870,6 +870,7 @@ LIB_OBJS += gpg-interface.o LIB_OBJS += graph.o LIB_OBJS += grep.o LIB_OBJS += hashmap.o +LIB_OBJS += linear-assignment.o LIB_OBJS += help.o LIB_OBJS += hex.o LIB_OBJS += ident.o diff --git a/linear-assignment.c b/linear-assignment.c new file mode 100644 index 0000000000..9b3e56e283 --- /dev/null +++ b/linear-assignment.c @@ -0,0 +1,201 @@ +/* + * Based on: Jonker, R., & Volgenant, A. (1987). <i>A shortest augmenting path + * algorithm for dense and sparse linear assignment problems</i>. Computing, + * 38(4), 325-340. + */ +#include "cache.h" +#include "linear-assignment.h" + +#define COST(column, row) cost[(column) + column_count * (row)] + +/* + * The parameter `cost` is the cost matrix: the cost to assign column j to row + * i is `cost[j + column_count * i]. + */ +void compute_assignment(int column_count, int row_count, int *cost, + int *column2row, int *row2column) +{ + int *v, *d; + int *free_row, free_count = 0, saved_free_count, *pred, *col; + int i, j, phase; + + memset(column2row, -1, sizeof(int) * column_count); + memset(row2column, -1, sizeof(int) * row_count); + ALLOC_ARRAY(v, column_count); + + /* column reduction */ + for (j = column_count - 1; j >= 0; j--) { + int i1 = 0; + + for (i = 1; i < row_count; i++) + if (COST(j, i1) > COST(j, i)) + i1 = i; + v[j] = COST(j, i1); + if (row2column[i1] == -1) { + /* row i1 unassigned */ + row2column[i1] = j; + column2row[j] = i1; + } else { + if (row2column[i1] >= 0) + row2column[i1] = -2 - row2column[i1]; + column2row[j] = -1; + } + } + + /* reduction transfer */ + ALLOC_ARRAY(free_row, row_count); + for (i = 0; i < row_count; i++) { + int j1 = row2column[i]; + if (j1 == -1) + free_row[free_count++] = i; + else if (j1 < -1) + row2column[i] = -2 - j1; + else { + int min = COST(!j1, i) - v[!j1]; + for (j = 1; j < column_count; j++) + if (j != j1 && min > COST(j, i) - v[j]) + min = COST(j, i) - v[j]; + v[j1] -= min; + } + } + + if (free_count == + (column_count < row_count ? row_count - column_count : 0)) { + free(v); + free(free_row); + return; + } + + /* augmenting row reduction */ + for (phase = 0; phase < 2; phase++) { + int k = 0; + + saved_free_count = free_count; + free_count = 0; + while (k < saved_free_count) { + int u1, u2; + int j1 = 0, j2, i0; + + i = free_row[k++]; + u1 = COST(j1, i) - v[j1]; + j2 = -1; + u2 = INT_MAX; + for (j = 1; j < column_count; j++) { + int c = COST(j, i) - v[j]; + if (u2 > c) { + if (u1 < c) { + u2 = c; + j2 = j; + } else { + u2 = u1; + u1 = c; + j2 = j1; + j1 = j; + } + } + } + if (j2 < 0) { + j2 = j1; + u2 = u1; + } + + i0 = column2row[j1]; + if (u1 < u2) + v[j1] -= u2 - u1; + else if (i0 >= 0) { + j1 = j2; + i0 = column2row[j1]; + } + + if (i0 >= 0) { + if (u1 < u2) + free_row[--k] = i0; + else + free_row[free_count++] = i0; + } + row2column[i] = j1; + column2row[j1] = i; + } + } + + /* augmentation */ + saved_free_count = free_count; + ALLOC_ARRAY(d, column_count); + ALLOC_ARRAY(pred, column_count); + ALLOC_ARRAY(col, column_count); + for (free_count = 0; free_count < saved_free_count; free_count++) { + int i1 = free_row[free_count], low = 0, up = 0, last, k; + int min, c, u1; + + for (j = 0; j < column_count; j++) { + d[j] = COST(j, i1) - v[j]; + pred[j] = i1; + col[j] = j; + } + + j = -1; + do { + last = low; + min = d[col[up++]]; + for (k = up; k < column_count; k++) { + j = col[k]; + c = d[j]; + if (c <= min) { + if (c < min) { + up = low; + min = c; + } + col[k] = col[up]; + col[up++] = j; + } + } + for (k = low; k < up; k++) + if (column2row[col[k]] == -1) + goto update; + + /* scan a row */ + do { + int j1 = col[low++]; + + i = column2row[j1]; + u1 = COST(j1, i) - v[j1] - min; + for (k = up; k < column_count; k++) { + j = col[k]; + c = COST(j, i) - v[j] - u1; + if (c < d[j]) { + d[j] = c; + pred[j] = i; + if (c == min) { + if (column2row[j] == -1) + goto update; + col[k] = col[up]; + col[up++] = j; + } + } + } + } while (low != up); + } while (low == up); + +update: + /* updating of the column pieces */ + for (k = 0; k < last; k++) { + int j1 = col[k]; + v[j1] += d[j1] - min; + } + + /* augmentation */ + do { + if (j < 0) + BUG("negative j: %d", j); + i = pred[j]; + column2row[j] = i; + SWAP(j, row2column[i]); + } while (i1 != i); + } + + free(col); + free(pred); + free(d); + free(v); + free(free_row); +} diff --git a/linear-assignment.h b/linear-assignment.h new file mode 100644 index 0000000000..1dfea76629 --- /dev/null +++ b/linear-assignment.h @@ -0,0 +1,22 @@ +#ifndef LINEAR_ASSIGNMENT_H +#define LINEAR_ASSIGNMENT_H + +/* + * Compute an assignment of columns -> rows (and vice versa) such that every + * column is assigned to at most one row (and vice versa) minimizing the + * overall cost. + * + * The parameter `cost` is the cost matrix: the cost to assign column j to row + * i is `cost[j + column_count * i]. + * + * The arrays column2row and row2column will be populated with the respective + * assignments (-1 for unassigned, which can happen only if column_count != + * row_count). + */ +void compute_assignment(int column_count, int row_count, int *cost, + int *column2row, int *row2column); + +/* The maximal cost in the cost matrix (to prevent integer overflows). */ +#define COST_MAX (1<<16) + +#endif |