A Randomized Polynomial Kernelization for Vertex Cover with a Smaller Parameter
نویسندگان
چکیده
منابع مشابه
A Randomized Polynomial Kernelization for Vertex Cover with a Smaller Parameter
In the vertex cover problem we are given a graph G = (V,E) and an integer k and have to determine whether there is a set X ⊆ V of size at most k such that each edge in E has at least one endpoint in X. The problem can be easily solved in time O∗(2k), making it fixed-parameter tractable (FPT) with respect to k. While the fastest known algorithm takes only time O∗(1.2738k), much stronger improvem...
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We revisit the topic of polynomial kernels for Vertex Cover relative to structural parameters. Our starting point is a recent paper due to Fomin and Str{\o}mme [WG 2016] who gave a kernel with $\mathcal{O}(|X|^{12})$ vertices when $X$ is a vertex set such that each connected component of $G-X$ contains at most one cycle, i.e., $X$ is a modulator to a pseudoforest. We strongly generalize this re...
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Kernelization is a concept that enables the formal mathematical analysis of data reduction through the framework of parameterized complexity. Intensive research into the Vertex Cover problem has shown that there is a preprocessing algorithm which given an instance (G, k) of Vertex Cover outputs an equivalent instance (G′, k′) in polynomial time with the guarantee that G′ has at most 2k′ vertice...
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The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter k. Besides being the basis for efficient parameterized algorithms, this method also provides a wealth of information to reason about in the context of constraint programming. We study the use of kernelization for designing propagators thro...
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For solving combinatorial optimisation problems, exactmethods accurately exploit the structure of the problem but are tractable only up to a certain size; approximation or heuristic methods are tractable for very large problems butmay possibly be led into a bad solution. A question that arises is, From where can we obtain knowledge of the problem structure via exact methods that can be exploite...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2018
ISSN: 0895-4801,1095-7146
DOI: 10.1137/16m1104585