文章基本信息

标题：Kernelizing the Hitting Set Problem in Linear Sequential and Constant Parallel Time
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作者：Max Bannach ; Malte Skambath ; Till Tantau 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：162
页码：9:1-9:16
DOI：10.4230/LIPIcs.SWAT.2020.9
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We analyze a reduction rule for computing kernels for the hitting set problem: In a hypergraph, the link of a set c of vertices consists of all edges that are supersets of c. We call such a set critical if its link has certain easy-to-check size properties. The rule states that the link of a critical c can be replaced by c. It is known that a simple linear-time algorithm for computing hitting set kernels (number of edges) at most k^d (k is the hitting set size, d is the maximum edge size) can be derived from this rule. We parallelize this algorithm and obtain the first ACâ° kernel algorithm that outputs polynomial-size kernels. Previously, such algorithms were not even known for artificial problems. An interesting application of our methods lies in traditional, non-parameterized approximation theory: Our results imply that uniform ACâ°-circuits can compute a hitting set whose size is polynomial in the size of an optimal hitting set.
关键词：Kernelization; Approximation; Hitting Set; Constant-Depth Circuits