License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.24
URN: urn:nbn:de:0030-drops-112394
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11239/
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Austrin, Per ; Stankovic, Aleksa

Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder

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LIPIcs-APPROX-RANDOM-2019-24.pdf (0.5 MB)


Abstract

Assuming the Unique Games Conjecture, we show that existing approximation algorithms for some Boolean Max-2-CSPs with cardinality constraints are optimal. In particular, we prove that Max-Cut with cardinality constraints is UG-hard to approximate within ~~0.858, and that Max-2-Sat with cardinality constraints is UG-hard to approximate within ~~0.929. In both cases, the previous best hardness results were the same as the hardness of the corresponding unconstrained Max-2-CSP (~~0.878 for Max-Cut, and ~~0.940 for Max-2-Sat).
The hardness for Max-2-Sat applies to monotone Max-2-Sat instances, meaning that we also obtain tight inapproximability for the Max-k-Vertex-Cover problem.

BibTeX - Entry

@InProceedings{austrin_et_al:LIPIcs:2019:11239,
  author =	{Per Austrin and Aleksa Stankovic},
  title =	{{Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11239},
  URN =		{urn:nbn:de:0030-drops-112394},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.24},
  annote =	{Keywords: Constraint satisfaction problems, global cardinality constraints, semidefinite programming, inapproximability, Unique Games Conjecture, Max-Cut, Max-}
}

Keywords: Constraint satisfaction problems, global cardinality constraints, semidefinite programming, inapproximability, Unique Games Conjecture, Max-Cut, Max-
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
Issue Date: 2019
Date of publication: 17.09.2019


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