Approximating Bounded Occurrence Ordering CSPs

A theorem of Hastad shows that for every constraint satisfaction problem (CSP) over a fixed size domain, instances where each variable appears in at most O(1) constraints admit a non-trivial approximation algorithm, in the sense that one can beat (by an additive constant) the approximation ratio achieved by the naive algorithm that simply picks a random assignment. We consider the analogous question for ordering CSPs, where the goal is to find a linear ordering of the variables to maximize the number of satisfied constraints, each of which stipulates some restriction on the local order of the involved variables. It was shown recently that without the bounded occurrence restriction, for every ordering CSP it is Unique Games-hard to beat the naive random ordering algorithm.