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

Per Austrin; Aleksa Stankovic

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arXiv · 1907.04165

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

Per Austrin·Aleksa Stankovic

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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 \approx 0.858, and that Max-2-Sat with cardinality constraints is UG-hard to approximate within \approx 0.929. In both cases, the previous best hardness results were the same as the hardness of the corresponding unconstrained Max-2-CSP (\approx 0.878 for Max-Cut, and \approx 0.940 for Max-2-Sat). The hardness obtained 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.

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Per Austrin, Aleksa Stankovic. 2019-07-09. Global Cardinality Constraints Make Approximating Some Max-2-CSPs Harder. https://arxiv.org/abs/1907.04165

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