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Approximation Algorithms and Lower Bounds for Graph Burning

Authors Matej Lieskovský , Jiří Sgall , Andreas Emil Feldmann

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Author Details

Matej Lieskovský
  • Faculty of Mathematics and Physics, Computer Science Institute of Charles University, Prague, Czech Republic
Jiří Sgall
  • Faculty of Mathematics and Physics, Computer Science Institute of Charles University, Prague, Czech Republic
Andreas Emil Feldmann
  • Department of Computer Science, University of Sheffield, UK

Funding

  • Lieskovský, Matej: Partially supported by GAUK project 234723, and GA ČR project 19-27871X.
  • Sgall, Jiří: Partially supported by GA ČR project 19-27871X.

Acknowledgements

We are grateful to anonymous referees for detailed reviews and helpful comments.

Cite AsGet BibTex

Matej Lieskovský, Jiří Sgall, and Andreas Emil Feldmann. Approximation Algorithms and Lower Bounds for Graph Burning. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.9

Abstract

Graph Burning models information spreading in a given graph as a process such that in each step one node is infected (informed) and also the infection spreads to all neighbors of previously infected nodes. Formally, given a graph G = (V,E), possibly with edge lengths, the burning number b(G) is the minimum number g such that there exist nodes v_0,…,v_{g-1} ∈ V satisfying the property that for each u ∈ V there exists i ∈ {0,…,g-1} so that the distance between u and v_i is at most i. We present a randomized 2.314-approximation algorithm for computing the burning number of a general graph, even with arbitrary edge lengths. We complement this by an approximation lower bound of 2 for the case of equal length edges, and a lower bound of 4/3 for the case when edges are restricted to have length 1. This improves on the previous 3-approximation algorithm and an APX-hardness result.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Graph Algorithms
  • approximation Algorithms
  • randomized Algorithms

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