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.2020.1
URN: urn:nbn:de:0030-drops-133043
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13304/
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Agrawal, Akanksha ; Ramanujan, M. S.

On the Parameterized Complexity of Clique Elimination Distance

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LIPIcs-IPEC-2020-1.pdf (0.6 MB)

Abstract

Bulian and Dawar [Algorithmica, 2016] introduced the notion of elimination distance in an effort to define new tractable parameterizations for graph problems and showed that deciding whether a given graph has elimination distance at most k to any minor-closed class of graphs is fixed-parameter tractable parameterized by k [Algorithmica, 2017].
In this paper, we consider the problem of computing the elimination distance of a given graph to the class of cluster graphs and initiate the study of the parameterized complexity of a more general version - that of obtaining a modulator to such graphs. That is, we study the (η,Clq)-Elimination Deletion problem ((η,Clq)-ED Deletion) where, for a fixed η, one is given a graph G and k ∈ ℕ and the objective is to determine whether there is a set S ⊆ V(G) such that the graph G-S has elimination distance at most η to the class of cluster graphs.
Our main result is a polynomial kernelization (parameterized by k) for this problem. As components in the proof of our main result, we develop a k^?(η k + η²)n^?(1)-time fixed-parameter algorithm for (η,Clq)-ED Deletion and a polynomial-time factor-min{?(η⋅ opt⋅ log² n),opt^?(1)} approximation algorithm for the same problem.

BibTeX - Entry

@InProceedings{agrawal_et_al:LIPIcs:2020:13304,
  author =	{Akanksha Agrawal and M. S. Ramanujan},
  title =	{{On the Parameterized Complexity of Clique Elimination Distance}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{1:1--1:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Yixin Cao and Marcin Pilipczuk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13304},
  URN =		{urn:nbn:de:0030-drops-133043},
  doi =		{10.4230/LIPIcs.IPEC.2020.1},
  annote =	{Keywords: Elimination Distance, Cluster Graphs, Kernelization}
}

Keywords: Elimination Distance, Cluster Graphs, Kernelization
Collection: 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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