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ECCC
2000

Improved Approximation of MAX-CUT on Graphs of Bounded Degree

9 years 8 months ago
Improved Approximation of MAX-CUT on Graphs of Bounded Degree
We analyze the addition of a simple local improvement step to various known randomized approximation algorithms. Let ' 0:87856 denote the best approximation ratio currently known for the Max Cut problem on general graphs GW95]. We consider a semide nite relaxation of the Max Cut problem, round it using the random hyperplane rounding technique of ( GW95]), and then add a local improvement step. We show that for graphs of degree at most , our algorithm achieves an approximation ratio of at least + , where > 0 is a constant that depends only on . In particular, using computer assisted analysis, we show that for graphs of maximal degree 3, our algorithm obtains an approximation ratio of at least 0:921, and for 3-regular graphs, the approximation ratio is at least 0:924. We note that for the semide nite relaxation of Max Cut used in GW95], the integrality gap is at least 1=0:884, even for 2-regular graphs.
Uriel Feige, Marek Karpinski, Michael Langberg
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2000
Where ECCC
Authors Uriel Feige, Marek Karpinski, Michael Langberg
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