Tight approximability of MAX 2-SAT and relatives, under UGC

Joshua Brakensiek, Neng Huang, Uri Zwick

Research output: Contribution to conferencePaperpeer-review

Abstract

Austrin showed that the approximation ratio β ≈ 0.94016567 obtained by the MAX 2-SAT approximation algorithm of Lewin, Livnat and Zwick (LLZ) is optimal modulo the Unique Games Conjecture (UGC) and modulo a Simplicity Conjecture that states that the worst performance of the algorithm is obtained on so called simple configurations. We prove Austrin's conjecture, thereby showing the optimality of the LLZ approximation algorithm, relying only on the Unique Games Conjecture. Our proof uses a combination of analytic and computational tools. We also present new approximation algorithms for two restrictions of the MAX 2-SAT problem. For MAX HORN-{1,2}-SAT, i.e., MAX CSP({x∨y,x̄∨y,x,x̄}), in which clauses are not allowed to contain two negated literals, we obtain an approximation ratio of 0.94615981. For MAX CSP({x ∨ y,x,x̄}), i.e., when 2-clauses are not allowed to contain negated literals, we obtain an approximation ratio of 0.95397990. By adapting Austrin's and our arguments for the MAX 2-SAT problem we show that these two approximation ratios are also tight, modulo only the UGC conjecture. This completes a full characterization of the approximability of the MAX 2-SAT problem and its restrictions.

Original languageEnglish
Pages1328-1344
Number of pages17
DOIs
StatePublished - 2024
Event35th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2024 - Alexandria, United States
Duration: 7 Jan 202410 Jan 2024

Conference

Conference35th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2024
Country/TerritoryUnited States
CityAlexandria
Period7/01/2410/01/24

Fingerprint

Dive into the research topics of 'Tight approximability of MAX 2-SAT and relatives, under UGC'. Together they form a unique fingerprint.

Cite this