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An Improved Approximation Algorithm for the Matching Augmentation Problem

Authors Joseph Cheriyan, Robert Cummings, Jack Dippel, Jasper Zhu

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Joseph Cheriyan
  • Comb. & Opt. Dept., University of Waterloo, Canada
Robert Cummings
  • Comb. & Opt. Dept., University of Waterloo, Canada
Jack Dippel
  • Mathematics & Statistics, McGill University, Montreal, Canada
Jasper Zhu
  • Comb. & Opt. Dept., University of Waterloo, Canada


We are grateful to several colleagues for their careful reading of preliminary drafts and for their comments.

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Joseph Cheriyan, Robert Cummings, Jack Dippel, and Jasper Zhu. An Improved Approximation Algorithm for the Matching Augmentation Problem. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 38:1-38:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • 2-Edge connected graph
  • 2-edge covers
  • approximation algorithms
  • connectivity augmentation
  • forest augmentation problem
  • matching augmentation problem
  • network design


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