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

Authors Per Austrin , Aleksa Stanković



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Author Details

Per Austrin
  • KTH Royal Institute of Technology, Stockholm, Sweden
Aleksa Stanković
  • KTH Royal Institute of Technology, Stockholm, Sweden

Acknowledgements

The authors thank Johan Håstad for helpful suggestions and comments on the manuscript. We also thank anonymous reviewers for their helpful remarks.

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Per Austrin and Aleksa Stanković. Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 24:1-24:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.24

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
  • Mathematics of computing → Approximation algorithms
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Constraint satisfaction problems
  • global cardinality constraints
  • semidefinite programming
  • inapproximability
  • Unique Games Conjecture
  • Max-Cut
  • Max-2-Sat

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