PHP Port of CAT_BAXTER's Python Hungarian Algorithm O(N^3). See: http://pastebin.com/tn6v0HDr

hungarian.php

<?php
function hungarian($matrix)
{
	$h = count($matrix);
	$w = count($matrix[0]);

	if ($h < $w)
	{
		for ($i = $h; $i < $w; ++$i)
		{
			$matrix[$i] = array_fill(0, $w, INF);
		}
	}
	elseif ($w < $h)
	{
		foreach ($matrix as &$row)
		{
			for ($i = $w; $i < $h; ++$i)
			{
				$row[$i] = INF;
			}
		}
	}

	$h = $w = max($h, $w);

	$u = array_fill(0, $h, 0);
	$v = array_fill(0, $w, 0);
	$ind = array_fill(0, $w, -1);

	foreach (range(0, $h - 1) as $i)
	{
		$links = array_fill(0, $w, -1);
		$mins = array_fill(0, $w, INF);
		$visited = array_fill(0, $w, false);

		$markedI = $i;
		$markedJ = -1;
		$j = 0;

		while (true)
		{
			$j = -1;

			foreach (range(0, $h - 1) as $j1)
			{
				if (!$visited[$j1])
				{
					$cur = $matrix[$markedI][$j1] - $u[$markedI] - $v[$j1];

					if ($cur < $mins[$j1])
					{
						$mins[$j1] = $cur;
						$links[$j1] = $markedJ;
					}

					if ($j == -1 || $mins[$j1] < $mins[$j])
					{
						$j = $j1;
					}
				}
			}

			$delta = $mins[$j];

			foreach (range(0, $w - 1) as $j1)
			{
				if ($visited[$j1])
				{
					$u[$ind[$j1]] += $delta;
					$v[$j1] -= $delta;
				}
				else
				{
					$mins[$j1] -= $delta;
				}
			}

			$u[$i] += $delta;

			$visited[$j] = true;

			$markedJ = $j;
			$markedI = $ind[$j];

			if ($markedI == -1)
			{
				break;
			}
		}

		while (true)
		{
			if ($links[$j] != -1)
			{
				$ind[$j] = $ind[$links[$j]];
				$j = $links[$j];
			}
			else
			{
				break;
			}
		}

		$ind[$j] = $i;
	}

	$result = array();

	foreach (range(0, $w - 1) as $j)
	{
		$result[$j] = $ind[$j];
	}

	return $result;
}

$m = [
		[  INF, 7858, 8743, 17325, 18510,  9231, 4920, 7056, 9701, 5034,  7825],
		[ 8128,  INF, 5021, 13603, 19635, 11386, 7075, 8840, 1843, 7189,  9256],
		[ 6809, 5364,  INF,  8582, 14614, 10067, 5756, 5904, 7207, 3882,  4235],
		[ 7849, 5515, 1040,   INF, 15654, 11107, 6796, 4713, 7358, 4900,  5275],
		[10918, 8365, 4109,  5808,   INF, 14176, 9865, 7928,  931, 7991,  8344],
		[  336, 7285, 2830, 11412, 17444,   INF, 4347, 6483, 6688, 4461,  7065],
		[ 1053, 2938, 3823, 12405, 15835,  4311,  INF, 2136, 4781,  114,  2905],
		[ 8930,  802, 5823, 14405, 20437, 12188, 7877,  INF, 2645, 7429, 10058],
		[ 9987, 7434, 3178, 11760, 17792, 13245, 8934, 6997,  INF, 7060,  7413],
		[10518, 2824, 3709, 12291, 15721, 13776, 9465, 2022, 4667,  INF,  7944],
		[ 2574, 4459, 5344,  9561, 17356,  5832, 1521, 3657, 6302, 1635,   INF]
];

print_r(hungarian($m));

Hey, I don't understand how you build the $m matrix. If I have this matrix:
10 9 5
9 8 3
6 4 7

How Do I build the $m matrix? (INF gets me confused). Thank you.