An Improved Approximation Algorithm for the Matching Augmentation Problem

TL;DR

This paper introduces a new approximation algorithm with a ratio of 5/3 for the matching augmentation problem, improving upon the previous 7/4 ratio, using novel algorithmic techniques that may benefit related problems.

Contribution

The paper presents a significantly improved 5/3-approximation algorithm for MAP, advancing the state-of-the-art in approximation ratios for this problem.

Findings

Achieved a 5/3 approximation ratio for MAP

Developed new algorithmic techniques for MAP

Potential for these techniques to impact related problems

Abstract

We present a $\frac53$-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 $\frac74$-approximation algorithm for the same problem was presented recently, see Cheriyan, et al., "The matching augmentation problem: a $\frac{7}{4}$-approximation algorithm," {\em Math. Program.}, 182(1):315--354, 2020; arXiv:1810.07816. Our improvement is based on new algorithmic techniques, and some of these may lead to advances on related problems.