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An FPT Algorithm for Elimination Distance to Bounded Degree Graphs

Authors Akanksha Agrawal , Lawqueen Kanesh , Fahad Panolan , M. S. Ramanujan , Saket Saurabh

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Author Details

Akanksha Agrawal
  • Indian Institute of Technology Madras, Chennai, India
Lawqueen Kanesh
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
Fahad Panolan
  • Indian Institute of Technology, Hyderabad, India
M. S. Ramanujan
  • University of Warwick, Coventry, UK
Saket Saurabh
  • University of Bergen, Norway
  • The Institute of Mathematical Sciences, HBNI, Chennai, India

Funding

  • Agrawal, Akanksha: Supported by New Faculty Initiative Grant, IIT Madras, Chennai, India.
  • Panolan, Fahad: Supported by Seed grant, IIT Hyderabad (SG/IITH/F224/2020-21/SG-79).
  • Ramanujan, M. S.: Supported by EPSRC grant EP/V007793/1.
  • Saurabh, Saket: Supported by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819416) and Swarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18.

Cite As Get BibTex

Akanksha Agrawal, Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, and Saket Saurabh. An FPT Algorithm for Elimination Distance to Bounded Degree Graphs. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 5:1-5:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.STACS.2021.5

Abstract

In the literature on parameterized graph problems, there has been an increased effort in recent years aimed at exploring novel notions of graph edit-distance that are more powerful than the size of a modulator to a specific graph class. In this line of research, Bulian and Dawar [Algorithmica, 2016] introduced the notion of elimination distance 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]. They showed that Graph Isomorphism parameterized by the elimination distance to bounded degree graphs is fixed-parameter tractable and asked whether determining the elimination distance to the class of bounded degree graphs is fixed-parameter tractable. Recently, Lindermayr et al. [MFCS 2020] obtained a fixed-parameter algorithm for this problem in the special case where the input is restricted to K₅-minor free graphs. 
In this paper, we answer the question of Bulian and Dawar in the affirmative for general graphs. In fact, we give a more general result capturing elimination distance to any graph class characterized by a finite set of graphs as forbidden induced subgraphs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Elimination Distance
  • Fixed-parameter Tractability
  • Graph Modification

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