Towards a unified theory of sparsification for matching problems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

In this paper, we present a construction of a “matching sparsifier”, that is, a sparse subgraph of the given graph that preserves large matchings approximately and is robust to modifications of the graph. We use this matching sparsifier to obtain several new algorithmic results for the maximum matching problem: ⁃ An almost (3/2)-approximation one-way communication protocol for the maximum matching problem, significantly simplifying the (3/2)-approximation protocol of Goel, Kapralov, and Khanna (SODA 2012) and extending it from bipartite graphs to general graphs. ⁃ An almost (3/2)-approximation algorithm for the stochastic matching problem, improving upon and significantly simplifying the previous 1.999-approximation algorithm of Assadi, Khanna, and Li (EC 2017). ⁃ An almost (3/2)-approximation algorithm for the fault-tolerant matching problem, which, to our knowledge, is the first non-trivial algorithm for this problem. Our matching sparsifier is obtained by proving new properties of the edge-degree constrained subgraph (EDCS) of Bernstein and Stein (ICALP 2015; SODA 2016) – designed in the context of maintaining matchings in dynamic graphs – that identifies EDCS as an excellent choice for a matching sparsifier. This leads to surprisingly simple and non-technical proofs of the above results in a unified way. Along the way, we also provide a much simpler proof of the fact that an EDCS is guaranteed to contain a large matching, which may be of independent interest.

Original languageEnglish (US)
Title of host publication2nd Symposium on Simplicity in Algorithms, SOSA 2019 - Co-located with the 30th ACM-SIAM Symposium on Discrete Algorithms, SODA 2019
EditorsJeremy T. Fineman, Michael Mitzenmacher
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770996
DOIs
StatePublished - Jan 2019
Event2nd Symposium on Simplicity in Algorithms, SOSA 2019 - San Diego, United States
Duration: Jan 8 2019Jan 9 2019

Publication series

NameOpenAccess Series in Informatics
Volume69
ISSN (Print)2190-6807

Conference

Conference2nd Symposium on Simplicity in Algorithms, SOSA 2019
Country/TerritoryUnited States
CitySan Diego
Period1/8/191/9/19

All Science Journal Classification (ASJC) codes

  • Geography, Planning and Development
  • Modeling and Simulation

Keywords

  • Fault-tolerant matching
  • Matching sparsifiers
  • Maximum matching
  • One-way communication complexity
  • Stochastic matching

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