Linear-programming design and analysis of fast algorithms for Max 2-CSP

The class Max (r, 2)-CSP (or simply Max 2-CSP) consists of constraint satisfaction problems with at most two r-valued variables per clause. For instances with n variables and m binary clauses, we present an O(nr5+19m/100 )-time algorithm which is the fastest polynomialspace algorithm for many problems in the class, including Max Cut. The method also proves a treewidth bound tw(G) ≤ (13/75 + o(1))m, which gives a faster Max 2-CSP algorithm that uses exponential space: running in time O⋆ (2(13/75+o(1))m ), this is fastest for most problems in Max 2-CSP. Parametrizing in terms of n rather than m, for graphs of average degree d we show a simple algorithm running time O⋆ 2(1− 2 d+1 )n , the fastest polynomial-space algorithm known. In combination with “Polynomial CSPs” introduced in a companion paper, these algorithms also allow (with an additional polynomial-factor overhead in space and time) counting and sampling, and the solution of problems like Max Bisection that escape the...

• Type: Journal
• Year: 2007
• Where: DISOPT
• Authors: Alexander D. Scott, Gregory B. Sorkin
• Keywords: Algorithms, Constraint Satisfaction Problems, DISOPT 2007, Max 2-CSP Algorithm