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.
@InProceedings{hsieh_et_al:LIPIcs.ICALP.2023.77, author = {Hsieh, Jun-Ting and Kothari, Pravesh K.}, title = {{Approximating Max-Cut on Bounded Degree Graphs: Tighter Analysis of the FKL Algorithm}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {77:1--77:7}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.77}, URN = {urn:nbn:de:0030-drops-181291}, doi = {10.4230/LIPIcs.ICALP.2023.77}, annote = {Keywords: Max-Cut, approximation algorithm, semidefinite programming} }
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