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An Improved Approximation Algorithm for the Matching Augmentation Problem

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

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)


Abstract
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.

Cite as

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)


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@InProceedings{cheriyan_et_al:LIPIcs.ISAAC.2021.38,
  author =	{Cheriyan, Joseph and Cummings, Robert and Dippel, Jack and Zhu, Jasper},
  title =	{{An Improved Approximation Algorithm for the Matching Augmentation Problem}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.38},
  URN =		{urn:nbn:de:0030-drops-154714},
  doi =		{10.4230/LIPIcs.ISAAC.2021.38},
  annote =	{Keywords: 2-Edge connected graph, 2-edge covers, approximation algorithms, connectivity augmentation, forest augmentation problem, matching augmentation problem, network design}
}
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