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New Upper Bounds for MaxSat

  • Rolf Niedermeier
  • Peter Rossmanith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1644)

Abstract

Given a boolean formula F in conjunctive normal form and an integer k, is there a truth assignment satisfying at least k clauses? This is the decision version of the Maximum Satisfiability (MaxSax) problem we study in this paper. We improve upper bounds on the worst case running time for MAXSAT. First, Cai and Chen showed that MAXSAT can be solved in time |F|2O(k) when the clause size is bounded by a constant. Imposing no restrictions on clause size, Mahajan and Raman and, independently, Dantsin et al. improved this to O(|F|⌽k), where ⌽ ≈ 1.6181 is the golden ratio. We present an algorithm running in time O(|F|1.3995k). The result extends to finding an optimal assignment and has several applications, in particular, for parameterized complexity and approximation algorithms. Moreover, if F has K clauses, we can find an optimal assignment in O(|F|1.3972K) steps and in O(1.1279|F|) steps, respectively. These are the fastest algorithm in the number of clauses and the length of the formula, respectively.

Keywords

Transformation Rule Vertex Cover Conjunctive Normal Form Truth Assignment Optimal Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Rolf Niedermeier
    • 1
  • Peter Rossmanith
    • 2
  1. 1.Wilhelm-Schickard-Institut für InformatikTübingenFederal Republic of Germany
  2. 2.Institut für InformatikTechnische Universität MünchenMünchenFederal Republic of Germany

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