Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach

Yuval Emek, Yuval Gil, Noga Harlev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Self-stabilization is an important concept in the realm of fault-tolerant distributed computing. In this paper, we propose a new approach that relies on the properties of linear programming duality to obtain self-stabilizing approximation algorithms for distributed graph optimization problems. The power of this new approach is demonstrated by the following results: A self-stabilizing 2(1 + ε)-approximation algorithm for minimum weight vertex cover that converges in O(log ∆/(ε log log ∆)) synchronous rounds. A self-stabilizing ∆-approximation algorithm for maximum weight independent set that converges in O(∆ + log n) synchronous rounds. A self-stabilizing ((2ρ + 1)(1 + ε))-approximation algorithm for minimum weight dominating set in ρ-arboricity graphs that converges in O((log ∆)/ε) synchronous rounds. In all of the above, ∆ denotes the maximum degree. Our technique improves upon previous results in terms of time complexity while incurring only an additive O(log n) overhead to the message size. In addition, to the best of our knowledge, we provide the first self-stabilizing algorithms for the weighted versions of minimum vertex cover and maximum independent set.

Original languageEnglish
Title of host publication26th International Conference on Principles of Distributed Systems, OPODIS 2022
EditorsEshcar Hillel, Roberto Palmieri, Etienne Riviere
ISBN (Electronic)9783959772655
DOIs
StatePublished - 1 Feb 2023
Event26th International Conference on Principles of Distributed Systems, OPODIS 2022 - Brussels, Belgium
Duration: 13 Dec 202215 Dec 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume253

Conference

Conference26th International Conference on Principles of Distributed Systems, OPODIS 2022
Country/TerritoryBelgium
CityBrussels
Period13/12/2215/12/22

Keywords

  • approximation algorithms
  • primal-dual
  • self-stabilization

All Science Journal Classification (ASJC) codes

  • Software

Fingerprint

Dive into the research topics of 'Design of Self-Stabilizing Approximation Algorithms via a Primal-Dual Approach'. Together they form a unique fingerprint.

Cite this