About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
Publication
Discrete Optimization
Paper
Linear-programming design and analysis of fast algorithms for Max 2-CSP
Abstract
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 (n r5 + 19 m / 100)-time algorithm which is the fastest polynomial-space 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{star operator} (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{star operator} (2(1 - frac(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 usual CSP framework. Linear programming is key to the design as well as the analysis of the algorithms. © 2007 Elsevier Ltd. All rights reserved.