linear-assignment: a function to solve least-cost assignment problems
The problem solved by the code introduced in this commit goes like this: given two sets of items, and a cost matrix which says how much it "costs" to assign any given item of the first set to any given item of the second, assign all items (except when the sets have different size) in the cheapest way. We use the Jonker-Volgenant algorithm to solve the assignment problem to answer questions such as: given two different versions of a topic branch (or iterations of a patch series), what is the best pairing of commits/patches between the different versions? Signed-off-by: Johannes Schindelin <johannes.schindelin@gmx.de> Signed-off-by: Junio C Hamano <gitster@pobox.com>
Johannes Schindelin committed
Aug 13, 2018 at 04:33 UTC
22d87333e5ee8871a9d42a15834ad91168a95928
3 files changed
+224
Makefile
+1
@@ -870,6 +870,7 @@ LIB_OBJS += gpg-interface.o
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LIB_OBJS += graph.o
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LIB_OBJS += grep.o
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LIB_OBJS += hashmap.o
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+LIB_OBJS += linear-assignment.o
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LIB_OBJS += help.o
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LIB_OBJS += hex.o
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LIB_OBJS += ident.o
linear-assignment.c
new
+201
@@ -0,0 +1,201 @@
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+/*
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+ * Based on: Jonker, R., & Volgenant, A. (1987). <i>A shortest augmenting path
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+ * algorithm for dense and sparse linear assignment problems</i>. Computing,
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+ * 38(4), 325-340.
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+ */
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+#include "cache.h"
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+#include "linear-assignment.h"
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+
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+#define COST(column, row) cost[(column) + column_count * (row)]
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+
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+/*
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+ * The parameter `cost` is the cost matrix: the cost to assign column j to row
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+ * i is `cost[j + column_count * i].
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+ */
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+void compute_assignment(int column_count, int row_count, int *cost,
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+ int *column2row, int *row2column)
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+{
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+ int *v, *d;
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+ int *free_row, free_count = 0, saved_free_count, *pred, *col;
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+ int i, j, phase;
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+
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+ memset(column2row, -1, sizeof(int) * column_count);
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+ memset(row2column, -1, sizeof(int) * row_count);
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+ ALLOC_ARRAY(v, column_count);
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+
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+ /* column reduction */
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+ for (j = column_count - 1; j >= 0; j--) {
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+ int i1 = 0;
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+
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+ for (i = 1; i < row_count; i++)
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+ if (COST(j, i1) > COST(j, i))
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+ i1 = i;
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+ v[j] = COST(j, i1);
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+ if (row2column[i1] == -1) {
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+ /* row i1 unassigned */
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+ row2column[i1] = j;
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+ column2row[j] = i1;
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+ } else {
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+ if (row2column[i1] >= 0)
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+ row2column[i1] = -2 - row2column[i1];
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+ column2row[j] = -1;
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+ }
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+ }
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+
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+ /* reduction transfer */
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+ ALLOC_ARRAY(free_row, row_count);
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+ for (i = 0; i < row_count; i++) {
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+ int j1 = row2column[i];
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+ if (j1 == -1)
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+ free_row[free_count++] = i;
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+ else if (j1 < -1)
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+ row2column[i] = -2 - j1;
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+ else {
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+ int min = COST(!j1, i) - v[!j1];
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+ for (j = 1; j < column_count; j++)
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+ if (j != j1 && min > COST(j, i) - v[j])
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+ min = COST(j, i) - v[j];
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+ v[j1] -= min;
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+ }
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+ }
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+
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+ if (free_count ==
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+ (column_count < row_count ? row_count - column_count : 0)) {
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+ free(v);
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+ free(free_row);
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+ return;
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+ }
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+
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+ /* augmenting row reduction */
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+ for (phase = 0; phase < 2; phase++) {
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+ int k = 0;
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+
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+ saved_free_count = free_count;
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+ free_count = 0;
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+ while (k < saved_free_count) {
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+ int u1, u2;
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+ int j1 = 0, j2, i0;
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+
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+ i = free_row[k++];
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+ u1 = COST(j1, i) - v[j1];
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+ j2 = -1;
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+ u2 = INT_MAX;
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+ for (j = 1; j < column_count; j++) {
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+ int c = COST(j, i) - v[j];
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+ if (u2 > c) {
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+ if (u1 < c) {
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+ u2 = c;
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+ j2 = j;
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+ } else {
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+ u2 = u1;
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+ u1 = c;
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+ j2 = j1;
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+ j1 = j;
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+ }
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+ }
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+ }
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+ if (j2 < 0) {
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+ j2 = j1;
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+ u2 = u1;
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+ }
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+
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+ i0 = column2row[j1];
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+ if (u1 < u2)
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+ v[j1] -= u2 - u1;
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+ else if (i0 >= 0) {
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+ j1 = j2;
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+ i0 = column2row[j1];
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+ }
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+
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+ if (i0 >= 0) {
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+ if (u1 < u2)
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+ free_row[--k] = i0;
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+ else
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+ free_row[free_count++] = i0;
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+ }
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+ row2column[i] = j1;
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+ column2row[j1] = i;
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+ }
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+ }
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+
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+ /* augmentation */
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+ saved_free_count = free_count;
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+ ALLOC_ARRAY(d, column_count);
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+ ALLOC_ARRAY(pred, column_count);
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+ ALLOC_ARRAY(col, column_count);
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+ for (free_count = 0; free_count < saved_free_count; free_count++) {
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+ int i1 = free_row[free_count], low = 0, up = 0, last, k;
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+ int min, c, u1;
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+
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+ for (j = 0; j < column_count; j++) {
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+ d[j] = COST(j, i1) - v[j];
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+ pred[j] = i1;
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+ col[j] = j;
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+ }
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+
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+ j = -1;
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+ do {
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+ last = low;
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+ min = d[col[up++]];
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+ for (k = up; k < column_count; k++) {
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+ j = col[k];
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+ c = d[j];
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+ if (c <= min) {
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+ if (c < min) {
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+ up = low;
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+ min = c;
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+ }
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+ col[k] = col[up];
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+ col[up++] = j;
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+ }
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+ }
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+ for (k = low; k < up; k++)
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+ if (column2row[col[k]] == -1)
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+ goto update;
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+
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+ /* scan a row */
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+ do {
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+ int j1 = col[low++];
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+
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+ i = column2row[j1];
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+ u1 = COST(j1, i) - v[j1] - min;
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+ for (k = up; k < column_count; k++) {
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+ j = col[k];
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+ c = COST(j, i) - v[j] - u1;
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+ if (c < d[j]) {
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+ d[j] = c;
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+ pred[j] = i;
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+ if (c == min) {
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+ if (column2row[j] == -1)
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+ goto update;
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+ col[k] = col[up];
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+ col[up++] = j;
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+ }
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+ }
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+ }
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+ } while (low != up);
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+ } while (low == up);
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+
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+update:
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+ /* updating of the column pieces */
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+ for (k = 0; k < last; k++) {
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+ int j1 = col[k];
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+ v[j1] += d[j1] - min;
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+ }
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+
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+ /* augmentation */
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+ do {
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+ if (j < 0)
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+ BUG("negative j: %d", j);
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+ i = pred[j];
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+ column2row[j] = i;
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+ SWAP(j, row2column[i]);
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+ } while (i1 != i);
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+ }
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+
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+ free(col);
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+ free(pred);
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+ free(d);
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+ free(v);
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+ free(free_row);
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+}
linear-assignment.h
new
+22
@@ -0,0 +1,22 @@
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+#ifndef LINEAR_ASSIGNMENT_H
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+#define LINEAR_ASSIGNMENT_H
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+
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+/*
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+ * Compute an assignment of columns -> rows (and vice versa) such that every
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+ * column is assigned to at most one row (and vice versa) minimizing the
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+ * overall cost.
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+ *
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+ * The parameter `cost` is the cost matrix: the cost to assign column j to row
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+ * i is `cost[j + column_count * i].
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+ *
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+ * The arrays column2row and row2column will be populated with the respective
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+ * assignments (-1 for unassigned, which can happen only if column_count !=
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+ * row_count).
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+ */
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+void compute_assignment(int column_count, int row_count, int *cost,
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+ int *column2row, int *row2column);
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+
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+/* The maximal cost in the cost matrix (to prevent integer overflows). */
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+#define COST_MAX (1<<16)
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+
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+#endif