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Algorithmica

, Volume 54, Issue 4, pp 472–489 | Cite as

Improved Parameterized Set Splitting Algorithms: A Probabilistic Approach

  • Jianer Chen
  • Songjian LuEmail author
Article

Abstract

In this paper, we study parameterized algorithms for the set splitting problem, for both weighted and unweighted versions. First, we develop a new and effective technique based on a probabilistic method that allows us to develop a simpler and more efficient deterministic kernelization algorithm for the unweighted set splitting problem. We then propose a randomized algorithm for the weighted set splitting problem that is based on a new subset partition technique and has its running time bounded by O *(2 k ), which is significantly better than that of the previous best deterministic algorithm (which only works for the simpler unweighted set splitting problem) of running time O *(2.65 k ). We also show that our algorithm can be de-randomized, which leads to a deterministic parameterized algorithm of running time O *(4 k ) for the weighted set splitting problem and gives the first proof that the problem is fixed-parameter tractable.

Keywords

Set splitting Randomized algorithm Derandomization Parametrized algorithm 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Computer ScienceTexas A&M UniversityCollege StationUSA

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