Distance Constraint Satisfaction Problems
Abstract
We study the complexity of constraint satisfaction problems for templates Γ that are firstorder definable in ({ Z}; {suc}), 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 NPcomplete.
 Publication:

Lecture Notes in Computer Science
 Pub Date:
 2010
 DOI:
 10.1007/9783642151552_16
 arXiv:
 arXiv:1004.3842
 Bibcode:
 2010LNCS.6281..162B
 Keywords:

 Computer Science  Computational Complexity;
 Computer Science  Logic in Computer Science;
 Mathematics  Logic
 EPrint:
 35 pages, 2 figures