Fixed Parameter Set Splitting, Linear Kernel and Improved Running Time
نویسندگان
چکیده
We study the problem k-Set Splitting in fixed parameter complexity. We show that the problem can be solved in time O∗(2.6494k), improving on the best currently known running time of O∗(8k). This is done by showing that a non-trivial instance must have a small minimal Set Cover, and using this to reduce the problem to a series of small instances of Max Sat. We also give a linear kernel containing 2k elements and 2k sets. This is done by reducing the problem to a bipartite graph problem where we use crown decomposition to reduce the graph. We show that this result also gives a good kernel for Max Cut.
منابع مشابه
Fixed Parameter Set Splitting , Obtaining a Linear Kernel and Improving Running Time
We study the problem k-SET SPLITTING from a Fixed Parameter point of view. We give a linear kernel of 2k elements and 2k sets and improve on the current best running time for the problem, giving a O∗(4k) algorithm. This is done by reducing the problem to a bipartite graph problem where we use crown decomposition to reduce the graph. We show that this result also gives a good kernel for Max Cut.
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We study the problem k-SET SPLITTING in fixed parameter complexity. We show that the problem can be solved in time O∗(2.6494k), improving on the best currently known running time of O∗(8k). This is done by showing that a non-trivial instance must have a small minimal SET COVER, and using this to reduce the problem to a series of small instances of MAX SAT. We also give a linear kernel containin...
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