An LP-Designed Algorithm for Constraint Satisfaction

The class Max (r, 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 ο~(r 19m/100 )-time algorithm. It is the fastest algorithm for most problems in the class (including Max Cut and Max 2-Sat), and in combination with Generalized CSPs introduced in a companion paper, also allows counting, 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 algorithm.

[1]  Gregory B. Sorkin,et al.  Generalized Constraint Satisfaction Problems , 2006 .

[2]  Peter Jonsson,et al.  An algorithm for counting maximum weighted independent sets and its applications , 2002, SODA '02.

[3]  P. Rossmanith,et al.  A New Satisabilit y Algorithm With Applications To Max-Cut , 2005 .

[4]  Edward A. Hirsch,et al.  A New Algorithm for MAX-2-SAT , 2000, STACS.

[5]  Uwe Schöning.  A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems , 1999, FOCS.

[6]  Luca Trevisan,et al.  The Approximability of Constraint Satisfaction Problems , 2001, SIAM J. Comput..

[7]  Nadia Creignou,et al.  A Dichotomy Theorem for Maximum Generalized Satisfiability Problems , 1995, J. Comput. Syst. Sci..

[8]  Alex D. Scott,et al.  Faster Algorithms for MAX CUT and MAX CSP, with Polynomial Expected Time for Sparse Instances , 2003, RANDOM-APPROX.

[9]  Rolf Niedermeier,et al.  Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT , 2003, Discret. Appl. Math..

[10]  Rolf Niedermeier,et al.  New Upper Bounds for Maximum Satisfiability , 2000, J. Algorithms.

[11]  David Eppstein,et al.  3-Coloring in Time O(1.3289^n) , 2000, J. Algorithms.

[12]  Luca Trevisan,et al.  Gadgets, Approximation, and Linear Programming , 2000, SIAM J. Comput..

[13]  Ryan Williams.  A new algorithm for optimal constraint satisfaction and its implications , 2004, Electron. Colloquium Comput. Complex..

[14]  Dániel Marx,et al.  Parameterized complexity of constraint satisfaction problems , 2004, Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004..