Proceedings
Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)
Optimal Inapproximability with Universal Factor Graphs
Pages 434 - 453
Abstract
The factor graph of an instance of a constraint satisfaction problem (CSP) is the bipartite graph indicating which variables appear in each constraint. An instance of the CSP is given by the factor graph together with a list of which predicate is applied for each constraint. We establish that many Max-CSPs remain as hard to approximate as in the general case even when the factor graph is fixed (depending only on the size of the instance) and known in advance.
Examples of results obtained for this restricted setting are:
1.
Optimal inapproximability for Max-3-Lin and Max-3-Sat (Håstad, J. ACM 2001).
2.
Approximation resistance for predicates supporting pairwise independent subgroups (Chan, J. ACM 2016).
3.
Hardness of the “(2 + ∊)-Sat” problem and other Promise CSPs (Austrin et al., SIAM J. Comput. 2017).
The main technical tool used to establish these results is a new way of folding the long code which we call “functional folding”.
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Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)
Pages: 434 - 453
Editor: Dániel Marx, CISPA Helmholtz Center for Information Security, Germany
ISBN (Online): 978-1-61197-646-5
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© 2021 by the Society for Industrial and Applied Mathematics.
History
Published online: 7 January 2021
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Cited By
- Dot-Product Proofs and Their Applications2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS) | 27 Oct 2024
- Max-3-Lin Over Non-abelian Groups with Universal Factor GraphsAlgorithmica, Vol. 85, No. 9 | 27 March 2023
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