TY - GEN

T1 - On the parameterized complexity of clique elimination distance

AU - Agrawal, Akanksha

AU - Ramanujan, M. S.

N1 - Funding Information:
Funding Akanksha Agrawal: supported by the PBC Program of Fellowships for Outstanding Postdoctoral Researchers from China and India when a part of the work was carried out.
Publisher Copyright:
© Akanksha Agrawal and M. S. Ramanujan;

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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 kO(ηk+η2)nO(1)-time fixed-parameter algorithm for (η, Clq)-ED Deletion and a polynomial-time factor-min{O(η · opt · log2 n), optO(1)} approximation algorithm for the same problem.

AB - 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 kO(ηk+η2)nO(1)-time fixed-parameter algorithm for (η, Clq)-ED Deletion and a polynomial-time factor-min{O(η · opt · log2 n), optO(1)} approximation algorithm for the same problem.

KW - Cluster Graphs

KW - Elimination Distance

KW - Kernelization

UR - http://www.scopus.com/inward/record.url?scp=85101449257&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.IPEC.2020.1

DO - 10.4230/LIPIcs.IPEC.2020.1

M3 - Conference contribution

AN - SCOPUS:85101449257

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 15th International Symposium on Parameterized and Exact Computation, IPEC 2020

A2 - Cao, Yixin

A2 - Pilipczuk, Marcin

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 15th International Symposium on Parameterized and Exact Computation, IPEC 2020

Y2 - 14 December 2020 through 18 December 2020

ER -