I have simple algorithmic question, but I can't find any source where this algorithm is explained in details.
Let's assume that we have incidence (with 0 and 1 values) matrix of size $m\times n$. Let we apply simultaneously all pairs of row $P_1 \in S_m$ and column $P_2 \in S_n$ permutations to this incidence matrix. Obviously because we have finite ordered set, there exist lexicographically largest value of this matrix.

Question is: **what is the best algorithm that allows to find this biggest value**?

Example input (Fano plane incidence matrix):
[![Fano plane][1]][1]

Example output:

$$
1110000 \\
1001100 \\
1000011 \\
0101010 \\
0100101 \\
0011001 \\
0010110
$$

  [1]: https://i.sstatic.net/j3pEv9Fd.png