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Self-Stabilizing Fully Adaptive Maximal Matching

Authors Shimon Bitton, Yuval Emek , Taisuke Izumi , Shay Kutten

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Author Details

Shimon Bitton
  • Intel Corporation, Haifa, Israel
Yuval Emek
  • Technion - Israel Institute of Technology, Haifa, Israel
Taisuke Izumi
  • Osaka Unversity, Japan
Shay Kutten
  • Technion - Israel Institute of Technology, Haifa, Israel

Funding

  • Emek, Yuval: supported by the Bernard M. Gordon Center for Systems Engineering at the Technion.
  • Izumi, Taisuke: supported by JSPS KAKENHI Grant Numbers 23H04385 and 22H03569.
  • Kutten, Shay: supported by ISF grant 1346/22 and by the Grand Technion Energy Program.

Cite As Get BibTex

Shimon Bitton, Yuval Emek, Taisuke Izumi, and Shay Kutten. Self-Stabilizing Fully Adaptive Maximal Matching. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 33:1-33:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.33

Abstract

A self-stabilizing randomized algorithm for mending maximal matching (MM) in synchronous networks is presented. Starting from a legal MM configuration and assuming that the network undergoes k faults or topology changes (that may occur in multiple batches), the algorithm is guaranteed to stabilize back to a legal MM configuration in time O(log k) in expectation and with high probability (in k), using constant size messages. The algorithm is simple to implement and is uniform in the sense that it does not assume unique identifiers, nor does it assume any global knowledge of the communication graph including its size. It relies on a generic probabilistic phase synchronization technique that may be useful for other self-stabilizing problems. The algorithm compares favorably with the existing self-stabilizing MM algorithms in terms of the dependence of its run-time on k, a.k.a. fully adaptive run-time. In fact, this dependence is asymptotically optimal for uniform algorithms that use constant size messages.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Fault-tolerant network topologies
Keywords
  • self-stabilization
  • maximal matching
  • fully adaptive run-time
  • dynamic graphs

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