文章基本信息

标题：A Randomized Polynomial Kernel for Subset Feedback Vertex Set
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作者：Eva-Maria C. Hols ; Stefan Kratsch
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：47
页码：43:1-43:14
DOI：10.4230/LIPIcs.STACS.2016.43
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The SUBSET FEEDBACK VERTEX SET problem generalizes the classical FEEDBACK VERTEX SET problem and asks, for a given undirected graph G=(V,E), a set S subseteq V, and an integer k, whether there exists a set X of at most k vertices such that no cycle in G-X contains a vertex of S. It was independently shown by Cygan et al. (ICALP'11, SIDMA'13) and Kawarabayashi and Kobayashi (JCTB'12) that SUBSET FEEDBACK VERTEX SET is fixed-parameter tractable for parameter k. Cygan et al. asked whether the problem also admits a polynomial kernelization. We answer the question of Cygan et al. positively by giving a randomized polynomial kernelization for the equivalent version where S is a set of edges. In a first step we show that EDGE SUBSET FEEDBACK VERTEX SET has a randomized polynomial kernel parameterized by |S|+k with O(|S|^2k) vertices. For this we use the matroid-based tools of Kratsch and Wahlstrom (FOCS'12). Next we present a preprocessing that reduces the given instance (G,S,k) to an equivalent instance (G',S',k') where the size of S' is bounded by O(k^4). These two results lead to a polynomial kernel for SUBSET FEEDBACK VERTEX SET with O(k^9) vertices.
关键词：parameterized complexity; kernelization; subset feedback vertex set