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Dynamic Maximal Matching in Clique Networks

Authors Minming Li, Peter Robinson, Xianbin Zhu

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • distributed graph algorithm
  • dynamic network
  • maximal matching
  • randomized algorithm
  • lower bound

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Abstract

We consider the problem of computing a maximal matching with a distributed algorithm in the presence of batch-dynamic changes to the graph topology. We assume that a graph of n nodes is vertex-partitioned among k players that communicate via message passing. Our goal is to provide an efficient algorithm that quickly updates the matching even if an adversary determines batches of 𝓁 edge insertions or deletions. We first show a lower bound of Ω((𝓁 log k)/(k²log n)) rounds for recomputing a matching assuming an oblivious adversary who is unaware of the initial (random) vertex partition as well as the current state of the players, and a stronger lower bound of Ω(𝓁/(klog n)) rounds against an adaptive adversary, who may choose any balanced (but not necessarily random) vertex partition initially and who knows the current state of the players. We also present a randomized algorithm that has an initialization time of O(n/(k log n)) rounds, while achieving an update time that that is independent of n: In more detail, the update time is O(⌈𝓁/k⌉ log k) against an oblivious adversary, who must fix all updates in advance. If we consider the stronger adaptive adversary, the update time becomes O (⌈𝓁/√k⌉ log k) rounds.

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Minming Li, Peter Robinson, and Xianbin Zhu. Dynamic Maximal Matching in Clique Networks. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 73:1-73:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ITCS.2024.73

Author Details

Minming Li
  • Department of Computer Science, City University of Hong Kong, Hong Kong
Peter Robinson
  • School of Computer & Cyber Sciences, Augusta University, GA, USA
Xianbin Zhu
  • Department of Computer Science, City University of Hong Kong, Hong Kong

Funding

The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. CityU 11213620].

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