Improved Algorithms for Weighted and Unweighted Set Splitting Problems

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*(2k), which even significantly improves the previously known upper bound for the unweigthed set splitting problem. We also show that our algorithm can be de-randomized, thus derive the first fixed parameter tractable algorithm for the weighted set splitting problem.

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