The complexity of packing edge-disjoint paths

Jan Dreier, Janosch Fuchs, Tim A. Hartmann, Philipp Kuinke, Peter Rossmanith, Bjoern Tauer, Hung Lung Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publication14th International Symposium on Parameterized and Exact Computation, IPEC 2019
EditorsBart M. P. Jansen, Jan Arne Telle
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771290
DOIs
Publication statusPublished - 2019 Dec
Event14th International Symposium on Parameterized and Exact Computation, IPEC 2019 - Munich, Germany
Duration: 2019 Sep 112019 Sep 13

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume148
ISSN (Print)1868-8969

Conference

Conference14th International Symposium on Parameterized and Exact Computation, IPEC 2019
Country/TerritoryGermany
CityMunich
Period2019/09/112019/09/13

Keywords

  • Covering
  • Embedding
  • Hamiltonian path
  • Packing
  • Parameterized complexity
  • Path-perfect graphs
  • Unary binpacking

ASJC Scopus subject areas

  • Software

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