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Distributed Maximum Matching Verification in CONGEST

Authors Mohamad Ahmadi, Fabian Kuhn

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Mohamad Ahmadi
  • University of Freiburg, Germany
Fabian Kuhn
  • University of Freiburg, Germany

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Mohamad Ahmadi and Fabian Kuhn. Distributed Maximum Matching Verification in CONGEST. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 37:1-37:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.DISC.2020.37

Abstract

We study the maximum cardinality matching problem in a standard distributed setting, where the nodes V of a given n-node network graph G = (V,E) communicate over the edges E in synchronous rounds. More specifically, we consider the distributed CONGEST model, where in each round, each node of G can send an O(log n)-bit message to each of its neighbors. We show that for every graph G and a matching M of G, there is a randomized CONGEST algorithm to verify M being a maximum matching of G in time O(|M|) and disprove it in time O(D + 𝓁), where D is the diameter of G and 𝓁 is the length of a shortest augmenting path. We hope that our algorithm constitutes a significant step towards developing a CONGEST algorithm to compute a maximum matching in time Õ(s^*), where s^* is the size of a maximum matching.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • distributed matching
  • distributed graph algorithms
  • augmenting paths

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