Distance constraint satisfaction problems

Bodirskya, Manuel, Dalmau, Victor, Martin, Barnaby, Mottet, Antoine and Pinsker, Michael (2016) Distance constraint satisfaction problems. Information and Computation, 247 . pp. 87-105. ISSN 0890-5401 [Article] (doi:10.1016/j.ic.2015.11.010)


We study the complexity of constraint satisfaction problems for templates Γ over the integers where the relations are first-order definable from the successor function. In the case that Γ is locally finite (i.e., the Gaifman graph of Γ has finite degree), we show that Γ is homomorphically equivalent to a structure with one of two classes of polymorphisms (which we call modular max and modular min) and the CSP for Γ can be solved in polynomial time, or Γ is homomorphically equivalent to a finite transitive structure, or the CSP for Γ is NP-complete. Assuming a widely believed conjecture from finite domain constraint satisfaction (we require the tractability conjecture by Bulatov, Jeavons and Krokhin in the special case of transitive finite templates), this proves that those CSPs have a complexity dichotomy, that is, are either in P or NP-complete.

Item Type: Article
Research Areas: A. > School of Science and Technology
A. > School of Science and Technology > Computer Science
Item ID: 21768
Depositing User: Jennifer Basford
Date Deposited: 08 May 2017 10:30
Last Modified: 25 Oct 2022 13:37
URI: https://eprints.mdx.ac.uk/id/eprint/21768

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