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Exact Max 2-Sat: Easier and Faster

  • Martin Fürer
  • Shiva Prasad Kasiviswanathan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4362)

Abstract

Prior algorithms known for exactly solving Max 2-Sat improve upon the trivial upper bound only for very sparse instances. We present new algorithms for exactly solving (in fact, counting) weighted Max 2-Sat instances. One of them has a good performance if the underlying constraint graph has a small separator decomposition, another has a slightly improved worst case performance. For a 2-Sat instance F with n variables, the worst case running time is \(\tilde{O}(2^{(1-1/(\tilde{d}(F)-1))n})\), where \(\tilde{d}(F)\) is the average degree in the constraint graph defined by F.

We use strict α-gadgets introduced by Trevisan, Sorkin, Sudan, and Williamson to get the same upper bounds for problems like Max 3-Sat and Max Cut. We also introduce a notion of strict (α,β)-gadget to provide a framework that allows composition of gadgets. This framework allows us to obtain the same upper bounds for Max k -Sat and Max k -Lin-2.

Keywords

Planar Graph Auxiliary Variable SIAM Journal Constraint Graph Prior Algorithm 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Martin Fürer
    • 1
  • Shiva Prasad Kasiviswanathan
    • 1
  1. 1.Computer Science and Engineering, Pennsylvania State University 

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