oizys/hungarian

Kuhn-Munkres (Hungarian) algorithm for the assignment problem

1.0.2 2026-02-07 19:06 UTC

Requires

• php: ^8.3

Requires (Dev)

• laravel/pint: ^1.25
• pestphp/pest: ^4.3
• phpstan/phpstan: ^2.1

MIT

README

Kuhn-Munkres (Hungarian) algorithm for the assignment problem in PHP. Solves optimal assignment in O(n^3) time.

Installation

composer require oizys/hungarian

Usage

use Oizys\Hungarian\Hungarian;

$solver = new Hungarian;

$result = $solver->solve([
    [82, 83, 69, 92],
    [77, 37, 49, 92],
    [11, 69,  5, 86],
    [ 8,  9, 98, 23],
]);

$result->cost();        // 140
$result->assignments(); // [[0, 2], [1, 1], [2, 0], [3, 3]]
$result->map();         // [0 => 2, 1 => 1, 2 => 0, 3 => 3]

count($result);         // 4
json_encode($result);   // {"assignments":[[0,2],[1,1],[2,0],[3,3]],"cost":140}
(string) $result;       // "4 assignments, cost: 140"

foreach ($result as $pair) {
    // [rowIndex, columnIndex]
}

Result implements Countable, IteratorAggregate, JsonSerializable, and Stringable.

Maximization

$solver = new Hungarian(Hungarian::MODE_MAXIMIZE);

Rectangular matrices

Matrices don't need to be square. Extra rows or columns are left unassigned automatically.

Forbidden assignments

Use INF to mark cells that must not be assigned:

$result = $solver->solve([
    [10,  2, INF, 15],
    [15, INF, INF,  2],
    [ 1, INF, INF,  4],
    [ 2, INF, INF, 10],
]);

Requirements

PHP 8.3+

License

MIT