I have a list of pairs of strings (or pairs of hashes) called V. I want to create a list W by removing elements from V such that W has as many pairs as possible and: There are no i,j such that W[i].first==W[j].first There are no i,j such that W[i].second==W[j].second I know it can be solved with max-flow, but the complexity would be at least O(|V|^2) because that would be the amount of edges in the graph. Is there any algorithm faster than that?, the algorithm might be probabilistic.
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This is literally maximum matching. But the complexity should be $$$O(V \sqrt{V})$$$ if one uses Dinic/Hopcroft-Karp for solving the maximum matching.
The amount of edges would be |V|.