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Matching Augmentation via Simultaneous Contractions

Authors Mohit Garg, Felix Hommelsheim, Nicole Megow

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Author Details

Mohit Garg
  • Department of Computer Science and Automation, Indian Institute of Science, Bengaluru, India
Felix Hommelsheim
  • Faculty of Mathematics and Computer Science, Universität Bremen, Germany
Nicole Megow
  • Faculty of Mathematics and Computer Science, Universität Bremen, Germany

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Mohit Garg, Felix Hommelsheim, and Nicole Megow. Matching Augmentation via Simultaneous Contractions. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 65:1-65:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We consider the matching augmentation problem (MAP), where a matching of a graph needs to be extended into a 2-edge-connected spanning subgraph by adding the minimum number of edges to it. We present a polynomial-time algorithm with an approximation ratio of 13/8 = 1.625 improving upon an earlier 5/3-approximation. The improvement builds on a new α-approximation preserving reduction for any α ≥ 3/2 from arbitrary MAP instances to well-structured instances that do not contain certain forbidden structures like parallel edges, small separators, and contractible subgraphs. We further introduce, as key ingredients, the technique of repeated simultaneous contractions and provide improved lower bounds for instances that cannot be contracted.

Subject Classification

ACM Subject Classification
  • Theory of computation → Routing and network design problems
  • matching augmentation
  • approximation algorithms
  • 2-edge-connectivity


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