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On the Parameterized Complexity of Clique Elimination Distance

Authors Akanksha Agrawal , M. S. Ramanujan

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Author Details

Akanksha Agrawal
  • Indian Institute of Technology Madras, Chennai, India
M. S. Ramanujan
  • University of Warwick, Coventry, UK

Funding

  • Agrawal, Akanksha: supported by the PBC Program of Fellowships for Outstanding Post-doctoral Researchers from China and India when a part of the work was carried out.

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Akanksha Agrawal and M. S. Ramanujan. On the Parameterized Complexity of Clique Elimination Distance. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.IPEC.2020.1

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^𝒪(η k + η²)n^𝒪(1)-time fixed-parameter algorithm for (η,Clq)-ED Deletion and a polynomial-time factor-min{𝒪(η⋅ opt⋅ log² n),opt^𝒪(1)} approximation algorithm for the same problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Elimination Distance
  • Cluster Graphs
  • Kernelization

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