License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2017.36
URN: urn:nbn:de:0030-drops-78769
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7876/
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Edwards, Katherine ; Muzi, Irene ; Wollan, Paul

Half-Integral Linkages in Highly Connected Directed Graphs

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LIPIcs-ESA-2017-36.pdf (0.5 MB)

Abstract

We study the half-integral k-Directed Disjoint Paths Problem (1/2 kDDPP) in highly strongly connected digraphs. The integral kDDPP is NP-complete even when restricted to instances where k=2, and the input graph is L-strongly connected, for any L >= 1. We show that when the integrality condition is relaxed to allow each vertex to be used in two paths, the problem becomes efficiently solvable in highly connected digraphs (even with k as part of the input).
Specifically, we show that there is an absolute constant c such that for each k >= 2 there exists L(k) such that 1/2 kDDPP is solvable in time O(|V(G)|^c) for a L(k)-strongly connected directed graph G. As the function L(k) grows rather quickly, we also show that 1/2 kDDPP is solvable in time O(|V(G)|^{f(k)}) in (36k^3+2k)-strongly connected directed graphs. We show that for each epsilon<1, deciding half-integral feasibility of kDDPP instances is NP-complete when k is given as part of the input, even when restricted to graphs with strong connectivity epsilon k.

BibTeX - Entry

@InProceedings{edwards_et_al:LIPIcs:2017:7876,
  author =	{Katherine Edwards and Irene Muzi and Paul Wollan},
  title =	{{Half-Integral Linkages in Highly Connected Directed Graphs}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{36:1--36:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Kirk Pruhs and Christian Sohler},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7876},
  URN =		{urn:nbn:de:0030-drops-78769},
  doi =		{10.4230/LIPIcs.ESA.2017.36},
  annote =	{Keywords: linkage, directed graph, treewidth}
}

Keywords: linkage, directed graph, treewidth
Collection: 25th Annual European Symposium on Algorithms (ESA 2017)
Issue Date: 2017
Date of publication: 01.09.2017

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