We study the complexity of constraint satisfaction problems for templates Γ that are first-order definable in (ℤ succ), the integers with the successor relation. 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), we provide a full classification for the case that Γ is locally finite (i.e., the Gaifman graph of Γ has finite degree). We show that one of the following is true: The structure Γ is homomorphically equivalent to a structure with a certain majority polymorphism (which we call modular median) and CSP(Γ) can be solved in polynomial time, or Γ is homomorphically equivalent to a finite transitive structure, or CSP(Γ) is NP-complete. © 2010 Springer-Verlag.
CITATION STYLE
Bodirsky, M., Dalmau, V., Martin, B., & Pinsker, M. (2010). Distance constraint satisfaction problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6281 LNCS, pp. 162–173). Springer Verlag. https://doi.org/10.1007/978-3-642-15155-2_16
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