A Simple 1-1/e Approximation for Oblivious Bipartite Matching
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We study the oblivious matching problem, which aims at finding a maximum matching on a graph with unknown edge set. Any algorithm for the problem specifies an ordering of the vertex pairs. The matching is then produced by probing the pairs following the ordering, and including a pair if both of them are unmatched and there exists an edge between them. The unweighted (Chan et al. (SICOMP 2018)) and the vertex-weighted (Chan et al. (TALG 2018)) versions of the problem are well studied. In this paper, we consider the edge-weighted oblivious matching problem on bipartite graphs, which generalizes the stochastic bipartite matching problem. Very recently, Gamlath et al. (SODA 2019) studied the stochastic bipartite matching problem, and proposed an (1-1/e)-approximate algorithm. We give a very simple algorithm adapted from the Ranking algorithm by Karp et al. (STOC 1990), and show that it achieves the same (1-1/e) approximation ratio for the oblivious matching problem on bipartite graph.
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