文章基本信息

标题：The Parameterized Complexity of the Minimum Shared Edges Problem
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作者：Till Fluschnik ; Stefan Kratsch ; Rolf Niedermeier 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：45
页码：448-462
DOI：10.4230/LIPIcs.FSTTCS.2015.448
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and sharing at most k edges. Herein, an edge is shared if it appears in at least two paths. We show that MSE is W[1]-hard when parameterized by the treewidth of the input graph and the number k of shared edges combined. We show that MSE is fixed-parameter tractable with respect to p, but does not admit a polynomial-size kernel (unless NP is a subset of coNP/poly). In the proof of the fixed-parameter tractability of MSE parameterized by p, we employ the treewidth reduction technique due to Marx, O'Sullivan, and Razgon [ACM TALG 2013].
关键词：Parameterized complexity; kernelization; treewidth; treewidth reduction