Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3

Cristina Bazgan, Zsolt Tuza

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The best approximation algorithm for Max Cut in graphs of maximum degree 3 uses semidefinite programming, has approximation ratio 0.9326, and its running time is Θ (n3.5 log n); but the best combinatorial algorithms have approximation ratio 4/5 only, achieved in O (n2) time [J.A. Bondy, S.C. Locke, J. Graph Theory 10 (1986) 477-504; E. Halperin, et al., J. Algorithms 53 (2004) 169-185]. Here we present an improved combinatorial approximation, which is a 5/6-approximation algorithm that runs in O (n2) time, perhaps improvable even to O (n). Our main tool is a new type of vertex decomposition for graphs of maximum degree 3.

Original languageEnglish
Pages (from-to)510-519
Number of pages10
JournalJournal of Discrete Algorithms
Volume6
Issue number3
DOIs
Publication statusPublished - Sep 2008

Keywords

  • Approximation algorithm
  • Cubic graph
  • Maximum cut
  • Unicyclic graph
  • Vertex decomposition

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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