Approximating Max-Cut on Bounded Degree Graphs: Tighter Analysis of the FKL Algorithm

06/18/2022

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by   Jun-Ting Hsieh, et al.

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In this note, we describe a α_GW + Ω̃(1/d^2)-factor approximation algorithm for Max-Cut on weighted graphs of degree ≤ d. Here, α_GW≈ 0.878 is the worst-case approximation ratio of the Goemans-Williamson rounding for Max-Cut. This improves on previous results for unweighted graphs by Feige, Karpinski, and Langberg and Florén. Our guarantee is obtained by a tighter analysis of the solution obtained by applying a natural local improvement procedure to the Goemans-Williamson rounding of the basic SDP strengthened with triangle inequalities.