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

Tuza, Zsolt; Bazgan, Cristina (2008), Combinatorial 5/6-approximation of Max Cut in graphs of maximum degree 3, Journal of Discrete Algorithms, 6, 3, p. 510-519. http://dx.doi.org/10.1016/j.jda.2007.02.002

Type
Article accepté pour publication ou publié
Date
2008
Journal name
Journal of Discrete Algorithms
Volume
6
Number
3
Publisher
Elsevier
Pages
510-519
Publication identifier
Metadata
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Author(s)
Tuza, Zsolt
Bazgan, Cristina
Abstract (EN)
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(n3.5logn); 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.
Subjects / Keywords
Maximum cut; Cubic graph; Approximation algorithm; Vertex decomposition; Unicyclic graph