License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.CCC.2020.9
URN: urn:nbn:de:0030-drops-125610
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Bhangale, Amey ; Khot, Subhash

Simultaneous Max-Cut Is Harder to Approximate Than Max-Cut

LIPIcs-CCC-2020-9.pdf (0.7 MB)


A systematic study of simultaneous optimization of constraint satisfaction problems was initiated by Bhangale et al. [ICALP, 2015]. The simplest such problem is the simultaneous Max-Cut. Bhangale et al. [SODA, 2018] gave a .878-minimum approximation algorithm for simultaneous Max-Cut which is almost optimal assuming the Unique Games Conjecture (UGC). For single instance Max-Cut, Goemans-Williamson [JACM, 1995] gave an α_GW-approximation algorithm where α_GW ≈ .87856720... which is optimal assuming the UGC.
It was left open whether one can achieve an α_GW-minimum approximation algorithm for simultaneous Max-Cut. We answer the question by showing that there exists an absolute constant ε₀ ≥ 10^{-5} such that it is NP-hard to get an (α_GW- ε₀)-minimum approximation for simultaneous Max-Cut assuming the Unique Games Conjecture.

BibTeX - Entry

  author =	{Amey Bhangale and Subhash Khot},
  title =	{{Simultaneous Max-Cut Is Harder to Approximate Than Max-Cut}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Shubhangi Saraf},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-125610},
  doi =		{10.4230/LIPIcs.CCC.2020.9},
  annote =	{Keywords: Simultaneous CSPs, Unique Games hardness, Max-Cut}

Keywords: Simultaneous CSPs, Unique Games hardness, Max-Cut
Collection: 35th Computational Complexity Conference (CCC 2020)
Issue Date: 2020
Date of publication: 17.07.2020
Supplementary Material:

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