文章基本信息

标题：Being Even Slightly Shallow Makes Life Hard
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作者：Irene Muzi ; Michael P. O'Brien ; Felix Reidl 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：83
页码：79:1-79:13
DOI：10.4230/LIPIcs.MFCS.2017.79
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study the computational complexity of identifying dense substructures, namely r/2-shallow topological minors and r-subdivisions. Of particular interest is the case r = 1, when these substructures correspond to very localized relaxations of subgraphs. Since Densest Subgraph can be solved in polynomial time, we ask whether these slight relaxations also admit efficient algorithms. In the following, we provide a negative answer: Dense r/2-Shallow Topological Minor and Dense r-Subdivsion are already NP-hard for r = 1 in very sparse graphs. Further, they do not admit algorithms with running time 2^(o(tw^2)) n^O(1) when parameterized by the treewidth of the input graph for r > 2 unless ETH fails.
关键词：Topological minors; NP Completeness; Treewidth; ETH; FPT algorithms