Approximation Algorithms and Lower Bounds for Graph Burning

Authors Matej Lieskovský , Jiří Sgall , Andreas Emil Feldmann

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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


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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)


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
  • Graph Algorithms
  • approximation Algorithms
  • randomized Algorithms


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