License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.FSTTCS.2015.448
URN: urn:nbn:de:0030-drops-56323
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5632/
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Fluschnik, Till ; Kratsch, Stefan ; Niedermeier, Rolf ; Sorge, Manuel

The Parameterized Complexity of the Minimum Shared Edges Problem

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Abstract

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].

BibTeX - Entry

@InProceedings{fluschnik_et_al:LIPIcs:2015:5632,
  author =	{Till Fluschnik and Stefan Kratsch and Rolf Niedermeier and Manuel Sorge},
  title =	{{The Parameterized Complexity of the Minimum Shared Edges Problem}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{448--462},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Prahladh Harsha and G. Ramalingam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5632},
  URN =		{urn:nbn:de:0030-drops-56323},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.448},
  annote =	{Keywords: Parameterized complexity, kernelization, treewidth, treewidth reduction}
}

Keywords: Parameterized complexity, kernelization, treewidth, treewidth reduction
Collection: 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)
Issue Date: 2015
Date of publication: 14.12.2015

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