LIMIT BEHAVIOR OF LOCALLY CONSISTENT CONSTRAINT SATISFACTION PROBLEMS

Abstract. An instance of a constraint satisfaction problem (CSP) is variable k-consistent if any subinstance with at most k variables has a solution. For a fixed constraint language L, ρk(L) is the largest ratio such that any variable k-consistent instance has a solution that satisfies at least a fraction of ρk(L) of the constraints. We provide an expression for the limit ρ(L): = limk→ ∞ ρk(L), and show that this limit coincides with the corresponding limit for constraint k-consistent instances, i.e., instances where all subinstances with at most k constraints have a solution. We also design an algorithm running in time polynomial in the size of input and 1/ε that for an input instance and a given ε either computes a solution that satisfies at least a fraction of ρ(L) − ε constraints or finds a set of inconsistent constraints whose size only depends on ǫ. Most of our results apply both to weighted and to unweighted instances of the constraint satisfaction problem. Key words. Constaint satisfaction problem (CSP), local consistenc

References

Limit behavior of locally consistent constraint satisfaction problems. (English summary