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Parameterized Complexity of Graph Burning

Authors Yasuaki Kobayashi , Yota Otachi

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Graph burning
  • parameterized complexity
  • fixed-parameter tractability

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Abstract

Graph Burning asks, given a graph G = (V,E) and an integer k, whether there exists (b₀,… ,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 arose by Kare and Reddy [IWOCA 2019] about 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. Although the parameterization by distance to split graphs cannot be handled with the clique-width argument, we show that this is also tractable by a reduction to a generalized problem with a smaller solution size.

Cite As Get BibTex

Yasuaki Kobayashi and Yota Otachi. Parameterized Complexity of Graph Burning. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 21:1-21:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.IPEC.2020.21

Author Details

Yasuaki Kobayashi
  • Kyoto University, Japan
Yota Otachi
  • Nagoya University, Japan

Funding

  • Kobayashi, Yasuaki: JSPS KAKENHI Grant Number JP20K19742.
  • Otachi, Yota: JSPS KAKENHI Grant Numbers JP18K11168, JP18K11169, JP18H04091.

Acknowledgements

The authors would like to thank Michael Lampis for bringing the Graph Burning problem to their attention.

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