Complexity and Approximability for Parameterized CSPs

The complexity of various Constraint Satisfaction Problems (CSP) when parameterized by structural measures (such as treewidth or clique-width) is a very well-investigated area. In this paper, we take a fresh look at such questions from the point of view of approximation, considering four standard CSP predicates: AND, OR, PARITY, and MAJORITY. By providing new or tighter hardness results for the satisfiability versions, as well as approximation algorithms for the corresponding maximization problems, we show that already these basic predicates display a diverse set of behaviors, ranging from being FPT to optimize exactly for quite general parameters (PARITY), to being W-hard but well-approximable (OR, MAJORITY) to being W-hard and inapproximable (AND). Our results indicate the interest in posing the question of approximability during the usual investigation of CSP complexity with regards to the landscape of structural parameters. 1998 ACM Subject Classification F.2.0