An Improved Approximation Algorithm for the Matching Augmentation Problem

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