On Approximability of Satisfiable 𝑘-CSPs: V
Name
3717823.3718127.pdf
Size
854.36 KB
Format
Adobe PDF
Checksum (MD5)
1f51a636922b603059b2d25cf35746fb
Author(s)
Bhangale, Amey
Khot, Subhash
Minzer, Dor
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
Amey Bhangale, Subhash Khot, and Dor Minzer. 2025. On Approximability of Satisfiable 𝑘-CSPs: V. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 62–71.
Version
Final published version
Abstract
We propose a framework of algorithm vs. hardness for all Max-CSPs and demonstrate it for a large class of predicates. This framework extends the work of Raghavendra [STOC, 2008], who showed a similar result for almost satisfiable Max-CSPs. Our framework is based on a new hybrid approximation algorithm, which uses a combination of the Gaussian elimination technique (i.e., solving a system of linear equations over an Abelian group) and the semidefinite programming relaxation. We complement our algorithm with a matching dictator vs. quasirandom test that has perfect completeness. The analysis of our dictator vs. quasirandom test is based on a novel invariance principle, which we call the mixed invariance principle. Our mixed invariance principle is an extension of the invariance principle of Mossel, O’Donnell and Oleszkiewicz [Annals of Mathematics, 2010] which plays a crucial role in Raghavendra’s work. The mixed invariance principle allows one to relate 3-wise correlations over discrete probability spaces with expectations over spaces that are a mixture of Guassian spaces and Abelian groups, and may be of independent interest.
Description
STOC ’25, Prague, Czechia
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3717823.3718127
