Solving minones-2-sat as Fast as vertex cover

  • Neeldhara Misra
  • N. S. Narayanaswamy
  • Venkatesh Raman
  • Bal Sri Shankar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6281)

Abstract

The problem of finding a satisfying assignment for a 2-SAT formula that minimizes the number of variables that are set to 1 (min ones 2–sat) is NP-complete. It generalizes the well-studied problem of finding the smallest vertex cover of a graph, which can be modeled using a 2-SAT formula with no negative literals. The natural parameterized version of the problem asks for a satisfying assignment of weight at most k.

In this paper, we present a polynomial-time reduction from min ones 2–sat to vertex cover without increasing the parameter and ensuring that the number of vertices in the reduced instance is equal to the number of variables of the input formula. Consequently, we conclude that this problem also has a simple 2-approximation algorithm and a 2k variables kernel subsuming these results known earlier. Further, the problem admits algorithms for the parameterized and optimization versions whose runtimes will always match the runtimes of the best-known algorithms for the corresponding versions of vertex cover.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Neeldhara Misra
    • 1
  • N. S. Narayanaswamy
    • 1
  • Venkatesh Raman
    • 1
  • Bal Sri Shankar
    • 1
  1. 1.Institute of Mathematical SciencesChennaiIndia

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