Local Search is Better than Random Assignment for Bounded Occurrence Ordering k-CSPs

We prove that the Bounded Occurrence Ordering k-CSP Problem is not approximation resistant. We give a very simple local search algorithm that always performs better than the random assignment algorithm (unless, the number of satisfied constraints does not depend on the ordering). Specifically, the expected value of the solution returned by the algorithm is at least Alg ≥ Avg+ α(B, k)(Opt −Avg), whereOpt is the value of the optimal solution; Avg is the expected value of the random solution; and α(B, k) = Ωk(B ) is a parameter depending only on k (the arity of the CSP) and B (the maximum number of times each variable is used in constraints). The question whether bounded occurrence ordering k-CSPs are approximation resistant was raised by Guruswami and Zhou (2012), who recently showed that bounded occurrence 3-CSPs and “monotone” k-CSPs admit a non-trivial approximation.