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URN: urn:nbn:de:0030-drops-55839
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Linear Kernels for Outbranching Problems in Sparse Digraphs

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Abstract

In the k-Leaf Out-Branching and k-Internal Out-Branching problems we are given a directed graph D with a designated root r and a nonnegative integer k. The question is to determine the existence of an outbranching rooted at r that has at least k leaves, or at least k internal vertices, respectively. Both these problems were intensively studied from the points of view of parameterized complexity and kernelization, and in particular for both of them kernels with O(k^2) vertices are known on general graphs. In this work we show that k-Leaf Out-Branching admits a kernel with O(k) vertices on H-minor-free graphs, for any fixed H, whereas k-Internal Out-Branching admits a kernel with O(k) vertices on any graph class of bounded expansion.

BibTeX - Entry

@InProceedings{bonamy_et_al:LIPIcs:2015:5583,
  author =	{Marthe Bonamy and Lukasz Kowalik and Michal Pilipczuk and Arkadiusz Socala},
  title =	{{Linear Kernels for Outbranching Problems in Sparse Digraphs}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{199--211},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Thore Husfeldt and Iyad Kanj},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5583},
  URN =		{urn:nbn:de:0030-drops-55839},
  doi =		{10.4230/LIPIcs.IPEC.2015.199},
  annote =	{Keywords: FPT algorithm, kernelization, outbranching, sparse graphs}
}

Keywords: FPT algorithm, kernelization, outbranching, sparse graphs
Seminar: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue date: 2015
Date of publication: 2015


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