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Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2020.9
URN: urn:nbn:de:0030-drops-125610
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12561/
Bhangale, Amey ;
Khot, Subhash
Simultaneous Max-Cut Is Harder to Approximate Than Max-Cut
Abstract
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
@InProceedings{bhangale_et_al:LIPIcs:2020:12561,
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 = {https://drops.dagstuhl.de/opus/volltexte/2020/12561},
URN = {urn:nbn:de:0030-drops-125610},
doi = {10.4230/LIPIcs.CCC.2020.9},
annote = {Keywords: Simultaneous CSPs, Unique Games hardness, Max-Cut}
}
