Parameterized Complexity of Graph Burning

Graph Burning asks, given a graph G = ( V , E ) and an integer k , whether there exists ( b 0 , ⋯ , b k - 1 ) ∈ V k such that every vertex in G has distance at most i from some b i . This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterize...

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Bibliographic Details
Published in:Algorithmica Vol. 84; no. 8; pp. 2379 - 2393
Main Authors: Kobayashi, Yasuaki, Otachi, Yota
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2022
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Complexity
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Mathematics of Computing
Parameterization
Parameters
Polynomials
Special Issue: Parameterized and Exact Computation (IPEC 2020)
Theory of Computation
Fixed-parameter tractability
Parameterized complexity
Graph burning
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:Graph Burning asks, given a graph G = ( V , E ) and an integer k , whether there exists ( b 0 , ⋯ , b k - 1 ) ∈ V k such that every vertex in G has distance at most i from some b i . This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterized complexity of this problem and answer all questions by Kare and Reddy [IWOCA 2019] about the parameterized complexity of the problem. We show that the problem is W[2]-complete parameterized by k and that it does not admit a polynomial kernel parameterized by vertex cover number unless NP ⊆ coNP / poly . We also show that the problem is fixed-parameter tractable parameterized by clique-width plus the maximum diameter among all connected components. This implies the fixed-parameter tractability parameterized by modular-width, by treedepth, and by distance to cographs. Using a different technique, we show that parameterization by distance to split graphs is also tractable. We finally show that the problem parameterized by max leaf number is XP.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-022-00962-8