A faster polynomial-space algorithm for Max 2-CSP

Faster Algorithms for MAX CUT and MAX CSP, with Polynomial Expected Time for Sparse Instances

We show that a random instance of a weighted maximum constraint satisfaction problem (or max 2-csp), whose clauses are over pairs of binary variables, is solvable by a deterministic algorithm in polynomial expected time, in the “sparse” regime where the expected number of clauses is half the number of variables. In particular, a maximum cut in a random graph with edge density 1/n or less can be...

A combinatorial algorithm for MAX CSP

We consider the problem MAX CSP over multi-valued domains with variables ranging over sets of size si s and constraints involving kj k variables. We study two algorithms with approximation ratios A and B, respectively, so we obtain a solution with approximation ratio max(A,B). The first algorithm is based on the linear programming algorithm of Serna, Trevisan, and Xhafa [Proc. 15th Annual Symp....

A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between

We introduce “hybrid” Max 2-CSP formulas consisting of “simple clauses”, namely conjunctions and disjunctions of pairs of variables, and general 2-variable clauses, which can be any integer-valued functions of pairs of boolean variables. This allows an algorithm to use both efficient reductions specific to AND and OR clauses, and other powerful reductions that require the general CSP setting. P...

Range-Based Algorithm for Max-CSP

Separate, Measure and Conquer: Faster Algorithms for Max 2-CSP and Counting Dominating Sets

We show a method resulting in the improvement of several polynomial-space, exponentialtime algorithms. An instance of the problem Max (r, 2)-CSP, or simply Max 2-CSP, is parametrized by the domain size r (often 2), the number of variables n (vertices in the constraint graph G), and the number of constraints m (edges in G). When G is cubic, and omitting sub-exponential terms here for clarity, we...