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

Authors Jun-Ting Hsieh, Pravesh K. Kothari

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Jun-Ting Hsieh
  • Carnegie Mellon University, Pittsburgh, PA, USA
Pravesh K. Kothari
  • Carnegie Mellon University, Pittsburgh, PA, USA


We thank Prasad Raghavendra for his Simons Institute talk on approximation algorithms for bounded degree constraint satisfaction problems and various related discussions that directly motivated this work. We thank Simons Institute Berkeley for hosting us in the Fall 2021 research program on Computational Complexity of Statistical Inference.

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Jun-Ting Hsieh and Pravesh K. Kothari. Approximating Max-Cut on Bounded Degree Graphs: Tighter Analysis of the FKL Algorithm. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 77:1-77:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


In this note, we describe a α_GW + Ω̃(1/d²)-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 [Feige et al., 2002] and Florén [Florén, 2016]. 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Max-Cut
  • approximation algorithm
  • semidefinite programming


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