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.2016.20
URN: urn:nbn:de:0030-drops-69345
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/6934/
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Kumar, Mithilesh ; Lokshtanov, Daniel

A 2lk Kernel for l-Component Order Connectivity

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LIPIcs-IPEC-2016-20.pdf (0.6 MB)

Abstract

In the l-Component Order Connectivity problem (l in N), we are given a graph G on n vertices, m edges and a non-negative integer k and asks whether there exists a set of vertices S subseteq V(G) such that |S| <= k and the size of the largest connected component in G-S is at most l. In this paper, we give a kernel for l-Component Order Connectivity with at most 2*l*k vertices that takes n^{O(l)} time for every constant l. On the way to obtaining our kernel, we prove a generalization of the q-Expansion Lemma to weighted graphs. This generalization may be of independent interest.

BibTeX - Entry

@InProceedings{kumar_et_al:LIPIcs:2017:6934,
  author =	{Mithilesh Kumar and Daniel Lokshtanov},
  title =	{{A 2lk Kernel for l-Component Order Connectivity}},
  booktitle =	{11th International Symposium on Parameterized and Exact Computation (IPEC 2016)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-023-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{63},
  editor =	{Jiong Guo and Danny Hermelin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/6934},
  URN =		{urn:nbn:de:0030-drops-69345},
  doi =		{10.4230/LIPIcs.IPEC.2016.20},
  annote =	{Keywords: Parameterized algorithms, Kernel, Component Order Connectivity, Max-min allocation, Weighted expansion}
}

Keywords: Parameterized algorithms, Kernel, Component Order Connectivity, Max-min allocation, Weighted expansion
Collection: 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)
Issue Date: 2017
Date of publication: 09.02.2017

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