jonkervolgenant.cpp

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This code implements the Jonker-Volgenant algorithm for the rectangular
assignment problem:

    R. Jonker and A. Volgenant. A Shortest Augmenting Path Algorithm for
    Dense and Sparse Linear Assignment Problems. *Computing*, 38:325-340
    December 1987.

The code is based on the pseudocode described in pages
1685-1686 of:

    DF Crouse. On implementing 2D rectangular assignment algorithms.
    IEEE Transactions on Aerospace and Electronic Systems
    52(4):1679-1696, August 2016
    doi: 10.1109/TAES.2016.140952

Author: PM Larsen
*/

#include <algorithm>
#include <vector>

static int augmenting_path(int nc, std::vector<double>& cost,
                           std::vector<double> &u, std::vector<double> &v,
                           std::vector<int> &path, std::vector<int> &row4col,
                           std::vector<double> &shortestPathCosts, int i,
                           std::vector<bool> &SR, std::vector<bool> &SC,
                           double *p_minVal) {
    double minVal = 0;

    int num_remaining = nc;
    std::vector<int> remaining(nc);
    std::iota(remaining.begin(), remaining.end(), 0);

    std::fill(SR.begin(), SR.end(), false);
    std::fill(SC.begin(), SC.end(), false);
    std::fill(shortestPathCosts.begin(), shortestPathCosts.end(), INFINITY);

    // find shortest augmenting path
    int sink = -1;
    while (sink == -1) {

        int index = -1;
        double lowest = INFINITY;

        for (int it = 0; it < num_remaining; it++) {
            int j = remaining[it];

            double r = minVal + cost[i * nc + j] - u[i] - v[j];
            if (r < shortestPathCosts[j]) {
                path[j] = i;
                shortestPathCosts[j] = r;
            }

            if (shortestPathCosts[j] < lowest
                || (shortestPathCosts[j] == lowest && row4col[j] == -1)) {
                lowest = shortestPathCosts[j];
                index = it;
            }
        }

        minVal = lowest;
        int j = remaining[index];
        if (minVal == INFINITY) // infeasible cost matrix
            return -1;

        if (row4col[j] == -1)
            sink = j;
        else
            i = row4col[j];

        SR[i] = true;
        SC[j] = true;
        remaining[index] = remaining[--num_remaining];
        remaining.resize(num_remaining);
    }

    *p_minVal = minVal;
    return sink;
}

static int _solve(int nr, int nc, double *input_cost,
                     int64_t *output_col4row) {

    // build a non-negative cost matrix
    std::vector<double> cost(nr * nc);
    double minval = *std::min_element(input_cost, input_cost + nr * nc);
    for (int i = 0; i < nr * nc; i++)
        cost[i] = input_cost[i] - minval;

    // initialize variables
    std::vector<double> u(nr, 0);
    std::vector<double> v(nc, 0);
    std::vector<double> shortestPathCosts(nc);
    std::vector<int> path(nc, -1);
    std::vector<int> col4row(nr, -1);
    std::vector<int> row4col(nc, -1);
    std::vector<bool> SR(nr);
    std::vector<bool> SC(nc);

    // iteratively build the solution
    for (int curRow = 0; curRow < nr; curRow++) {

        double minVal;
        int sink = augmenting_path(nc, cost, u, v, path, row4col,
                                   shortestPathCosts, curRow, SR, SC, &minVal);
        if (sink < 0)
            return -1;

        // update dual variables
        u[curRow] += minVal;
        for (int i = 0; i < nr; i++)
            if (SR[i] && i != curRow)
                u[i] += minVal - shortestPathCosts[col4row[i]];

        for (int i = 0; i < nc; i++)
            if (SC[i])
                v[i] -= minVal - shortestPathCosts[i];

        // augment previous solution
        int j = sink;
        while (1) {
            int i = path[j];
            row4col[j] = i;
            std::swap(col4row[i], j);
            if (i == curRow)
                break;
        }
    }

    for (int i = 0; i < nr; i++)
        output_col4row[i] = col4row[i];

    return 0;
}

#ifdef __cplusplus
extern "C" {
#endif

int solve_jonker_volgenant(int nr, int nc, double *input_cost,
                              int64_t *col4row) {
    return _solve(nr, nc, input_cost, col4row);
}

#ifdef __cplusplus
}
#endif