License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.77
URN: urn:nbn:de:0030-drops-181291
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18129/
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Hsieh, Jun-Ting ; Kothari, Pravesh K.

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

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Abstract

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.

BibTeX - Entry

@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/opus/volltexte/2023/18129},
  URN =		{urn:nbn:de:0030-drops-181291},
  doi =		{10.4230/LIPIcs.ICALP.2023.77},
  annote =	{Keywords: Max-Cut, approximation algorithm, semidefinite programming}
}

Keywords: Max-Cut, approximation algorithm, semidefinite programming
Collection: 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)
Issue Date: 2023
Date of publication: 05.07.2023


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