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.IPEC.2019.10
URN: urn:nbn:de:0030-drops-114710
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11471/
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Dreier, Jan ; Fuchs, Janosch ; Hartmann, Tim A. ; Kuinke, Philipp ; Rossmanith, Peter ; Tauer, Bjoern ; Wang, Hung-Lung

The Complexity of Packing Edge-Disjoint Paths

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LIPIcs-IPEC-2019-10.pdf (0.8 MB)


Abstract

We introduce and study the complexity of Path Packing. Given a graph G and a list of paths, the task is to embed the paths edge-disjoint in G. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is efficiently solvable for graphs of small treewidth, we study how this result translates to the much more general Path Packing. On the positive side, we give an FPT-algorithm on trees for the number of paths as parameter. Further, we give an XP-algorithm with the combined parameters maximal degree, number of connected components and number of nodes of degree at least three. Surprisingly the latter is an almost tight result by runtime and parameterization. We show an ETH lower bound almost matching our runtime. Moreover, if two of the three values are constant and one is unbounded the problem becomes NP-hard. Further, we study restrictions to the given list of paths. On the positive side, we present an FPT-algorithm parameterized by the sum of the lengths of the paths. Packing paths of length two is polynomial time solvable, while packing paths of length three is NP-hard. Finally, even the spacial case Exact Path Packing where the paths have to cover every edge in G exactly once is already NP-hard for two paths on 4-regular graphs.

BibTeX - Entry

@InProceedings{dreier_et_al:LIPIcs:2019:11471,
  author =	{Jan Dreier and Janosch Fuchs and Tim A. Hartmann and Philipp Kuinke and Peter Rossmanith and Bjoern Tauer and Hung-Lung Wang},
  title =	{{The Complexity of Packing Edge-Disjoint Paths}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Bart M. P. Jansen and Jan Arne Telle},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11471},
  URN =		{urn:nbn:de:0030-drops-114710},
  doi =		{10.4230/LIPIcs.IPEC.2019.10},
  annote =	{Keywords: parameterized complexity, embedding, packing, covering, Hamiltonian path, unary binpacking, path-perfect graphs}
}

Keywords: parameterized complexity, embedding, packing, covering, Hamiltonian path, unary binpacking, path-perfect graphs
Collection: 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)
Issue Date: 2019
Date of publication: 04.12.2019


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