An Improved Approximation Algorithm for the Matching Augmentation Problem

We present a 5 3 -approximation algorithm for the matching augmentation problem (MAP): given a multi-graph with edges of cost either zero or one such that the edges of cost zero form a matching, find a 2-edge connected spanning subgraph (2-ECSS) of minimum cost. A 7 4 -approximation algorithm for the same problem was presented recently, see Cheriyan, et al., “The matching augmentation problem: a 7 4 -approximation algorithm,” Math. Program., 182(1):315–354, 2020. Our improvement is based on new algorithmic techniques, and some of these may lead to advances on related problems.

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