Faster Exponential-Time Algorithms for Max 2-Sat, Max Cut, and Max k-Cut

A recent line of research has been to speed up exponential-time algorithms (deterministic or randomized) for maximization problems such as Max 2-Sat and Max Cut. The fastest previous algorithms run in time Õ(2m/5) for a Max 2-Sat instance with m clauses, and Õ(2m/4) for a Max Cut instance with n vertices and m edges (by applying the Max 2-Sat algorithm to a transformation of the graph). In this paper, we work with a larger class of problems, “Max (r, 2)-CSP”. We give a deterministic algorithm which solves any m-constraint Max (r, 2)-CSP instance in time Õ(r19m/100) (i.e., Õ(rm/5.26···)) and space O(mn). In particular, in time Õ(219m/100) we can solve Max Cut, Max Dicut, Max 2-Lin, Max 2-Sat, Max-Ones-2-Sat, maximum independent set, and minimum dominating set, and in time Õ(k19m/100) we can solve Max k-Cut; weighted versions of any of these problems can be accommodated at no extra cost. The algorithm is relatively simple, using just two transformation rules and one splitting rule, and the analysis hinges on a small linear program.

By: Alexander D. Scott; Gregory B. Sorkin

Published in: RC23457 in 2004


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