Improved Parameterized Algorithms for Weighted 3-Set Packing
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
An O*(3.523k) parameterized algorithm for 3-set packing
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
An O*(3.533k)-time parameterized algorithm for the 3-set packing problem
Theoretical Computer Science
Matching and P2-packing: weighted versions
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Matching and Weighted P2-Packing: Algorithms and Kernels
Theoretical Computer Science
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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.