Re: Problem on an nxn grid

You can formulate this problem as an instance of maximum weighted
matching on general graphs, which has efficient polynomial solvers.
The algorithm is:

- You first bring the matrix to upper triangular form (for every (i,j)
(i<j), a'_{ij} = M-min(a_{ij},a_{ji}), where M is a big number st
a'_{ij}>=0.
- Then form a graph with n nodes representing coordinates. Place edges
between nodes i and j (i<j) with weight a'_{ij}.
- Do maximum weighted matching on this graph.

Hope this helps.

Ali

.

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