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/*
* 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;
if (column_count < 2) {
memset(column2row, 0, sizeof(int) * column_count);
memset(row2column, 0, sizeof(int) * row_count);
return;
}
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);
}