Alternative polynomial-time algorithm for Bipartite Matching

11/01/2022

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by   Sylvain Guillemot, et al.

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If G is a bipartite graph, Hall's theorem <cit.> gives a condition for the existence of a matching of G covering one side of the bipartition. This theorem admits a well-known algorithmic proof involving the repeated search of augmenting paths. We present here an alternative algorithm, using a game-theoretic formulation of the problem. We also show how to extend this formulation to the setting of balanced hypergraphs.