Distance Constraint Satisfaction Problems

We study the complexity of constraint satisfaction problems for templates Gamma 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 Bulatov. Jeavons and krokhin in the special case of transitive finite templates) we provide a full classification for the case that Gamma is locally finite e, the Gaifman graph of F has finite degree) We show that one of the following IS true The structure Gamma is homomorphically equivalent to a structure with a certain majority polymorphism (which we call modular median) and CSP(Gamma) can be solved in polynomial time, or Gamma is homomorphically equivalent to a finite transitive structure, or CSP(Gamma) is NP-complete