TY - GEN
T1 - An FPT 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 - Publisher Copyright:
© Akanksha Agrawal, Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, and Saket Saurabh; licensed under Creative Commons License CC-BY 4.0.
PY - 2021/3/1
Y1 - 2021/3/1
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, 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.
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, 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.
KW - Elimination Distance
KW - Fixed-parameter Tractability
KW - Graph Modification
UR - http://www.scopus.com/inward/record.url?scp=85115261126&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.STACS.2021.5
DO - 10.4230/LIPIcs.STACS.2021.5
M3 - Conference contribution
AN - SCOPUS:85115261126
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021
A2 - Blaser, Markus
A2 - Monmege, Benjamin
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021
Y2 - 16 March 2021 through 19 March 2021
ER -