Constraints, MMSNP and expander relational structures

Abstract

We give a poly-time construction for a combinatorial classic known as Sparse Incomparability Lemma, studied by Erdős, Lovász, Nešetřil, Rödl and others: We show that every Constraint Satisfaction Problem is poly-time equivalent to its restriction to structures with large girth. This implies that the complexity classes CSP and Monotone Monadic Strict NP introduced by Feder and Vardi are computationally equivalent. The technical novelty of the paper is a concept of expander relations and a new type of product for relational structures: a generalization of the zig-zag product, the twisted product.

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Correspondence to Gábor Kun.

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This research was supported by OTKA Grants no. T043671 and NK 67867, Subhash Khot’s NSF Waterman Award CCF-1061938 and the MTA Rényi “Lendület” Groups and Graphs Research Group.

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Kun, G. Constraints, MMSNP and expander relational structures. Combinatorica 33, 335–347 (2013). https://doi.org/10.1007/s00493-013-2405-4

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