TY - JOUR

T1 - A FIXED-PARAMETER TRACTABLE ALGORITHM for ELIMINATION DISTANCE to BOUNDED DEGREE GRAPHS

AU - Agrawal, Akanksha

AU - Kanesh, Lawqueen

AU - Panolan, Fahad

AU - Ramanujan, M. S.

AU - Saurabh, Saket

N1 - Funding Information:
\ast Received by the editors February 3, 2021; accepted for publication (in revised form) November 10, 2021; published electronically April 7, 2022. Extended abstract appeared at STACS 2021 [LIPIcs Leibniz Int. Proc. Inform. 187, Wadern, Germany, 2021, 5]. \bfF \bfu \bfn \bfd \bfi \bfn \bfg : Agrawal is supported by New Faculty Initiation Grant IIT Madras. Panolan is supported by Seed grant, IIT Hyderabad (SG/IITH/F224/2020-21/SG-79). Ramanujan is supported by Engineering and Physical Sciences Research Council's New Investigator Award (EP/V007793/1). Saurabh is supported by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement 819416); and he also acknowledges the support of Swarnajayanti Fellowship grant DST/SJF/MSA-01/2017-18. https://doi.org/10.1137/21M1396824 \dagger Indian Institute of Technology Madras, Chennai, India (akanksha@cse.iitm.ac.in). \ddagger National University of Singapore, Singapore (lawqueen@comp.nus.edu.sg). \S Indian Institute of Technology, Hyderabad, India (panolan@iith.ac.in). \P University of Warwick, Warwick, UK (r.maadapuzhi-sridharan@warwick.ac.uk). \| University of Bergen, Norway and Institute of Mathematical Sciences, HBNI, India (saket@imsc. res.in).
Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics

PY - 2022/1/1

Y1 - 2022/1/1

N2 - 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, 75 (2016), pp. 363-382] 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, 79 (2017), pp. 139-158]. 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, Siebertz, and Vigny [MFCS 2020, LIPIcs Leibniz Int. Proc. Inform. 170, Wadern Germany, 2020, 65] 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.

AB - 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, 75 (2016), pp. 363-382] 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, 79 (2017), pp. 139-158]. 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, Siebertz, and Vigny [MFCS 2020, LIPIcs Leibniz Int. Proc. Inform. 170, Wadern Germany, 2020, 65] 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.

KW - elimination distance

KW - fixed-parameter tractability

KW - graph modification

UR - http://www.scopus.com/inward/record.url?scp=85130591302&partnerID=8YFLogxK

U2 - 10.1137/21M1396824

DO - 10.1137/21M1396824

M3 - Article

AN - SCOPUS:85130591302

VL - 36

SP - 911

EP - 921

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

SN - 0895-4801

IS - 2

ER -