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Deterministic Approximation Algorithm for Graph Burning

Author Matej Lieskovský

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Subject Classification

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

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Abstract

Graph Burning models a contagion spreading in a network as a process such that in each step one node is infected and also the infection spreads to all neighbors of previously infected nodes. Formally, the burning number b(G) of a given graph G = (V,E), possibly with edge lengths, is the minimum number g such that there exists a sequence of nodes v₁,…,v_g satisfying the property that for each w ∈ V there exists i ∈ {1,…,g} so that the distance between w and v_i is at most g-i.
We present an elegant deterministic 2.314-approximation algorithm for the Graph Burning problem on general graphs with arbitrary edge lengths. This algorithm matches the approximation ratio of the previous randomized 2.314-approximation algorithm and improves on the previous deterministic 3-approximation algorithm.

Cite As Get BibTex

Matej Lieskovský. Deterministic Approximation Algorithm for Graph Burning. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 108:1-108:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.108

Author Details

Matej Lieskovský
  • Faculty of Mathematics and Physics, Computer Science Institute of Charles University, Prague, Czech Republic

Funding

  • Lieskovský, Matej: Supported by GAUK project 234723, GA ČR project 19-27871X, and the grant SVV–2025–260822.

Acknowledgements

We wish to thank our reviewers and colleagues for their insightful feedback.

References

  1. Anthony Bonato, Jeannette Janssen, and Elham Roshanbin and. How to burn a graph. Internet Mathematics, 12(1-2):85-100, 2016. URL: https://doi.org/10.1080/15427951.2015.1103339.
  2. Anthony Bonato, Jeannette Janssen, and Elham Roshanbin. Burning a graph as a model of social contagion. In Anthony Bonato, Fan Chung Graham, and Paweł Prałat, editors, Algorithms and Models for the Web Graph, volume 8882, pages 13-22, Cham, December 2014. Springer International Publishing. URL: https://doi.org/10.1007/978-3-319-13123-8_2.
  3. Anthony Bonato and Shahin Kamali. Approximation algorithms for graph burning. In T.V. Gopal and Junzo Watada, editors, Theory and Applications of Models of Computation, pages 74-92, Cham, 2019. Springer International Publishing. URL: https://doi.org/10.1007/978-3-030-14812-6_6.
  4. Anthony Bonato and Thomas Lidbetter. Bounds on the burning numbers of spiders and path-forests. Theoretical Computer Science, 794:12-19, 2019. Special Issue on Theory and Applications of Graph Searching. URL: https://doi.org/10.1016/j.tcs.2018.05.035.
  5. Jesús García-Díaz, Julio César Pérez-Sansalvador, Lil María Xibai Rodríguez-Henríquez, and José Alejandro Cornejo-Acosta. Burning graphs through farthest-first traversal. IEEE Access, 10:30395-30404, 2022. URL: https://doi.org/10.1109/ACCESS.2022.3159695.
  6. Leszek Gąsieniec, Benjamin Smith, and Sebastian Wild. Towards the 5/6-Density Conjecture of Pinwheel Scheduling, pages 91-103. Society for Industrial and Applied Mathematics, 2022. URL: https://doi.org/10.1137/1.9781611977042.8.
  7. Felix Höhne and Rob van Stee. A 10/7-Approximation for Discrete Bamboo Garden Trimming and Continuous Trimming on Star Graphs. In Nicole Megow and Adam Smith, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023), volume 275 of Leibniz International Proceedings in Informatics (LIPIcs), pages 16:1-16:19, Dagstuhl, Germany, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.16.
  8. Akitoshi Kawamura. Proof of the density threshold conjecture for pinwheel scheduling. In Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, pages 1816-1819, New York, NY, USA, 2024. Association for Computing Machinery. URL: https://doi.org/10.1145/3618260.3649757.
  9. John Kuszmaul. Bamboo trimming revisited: Simple algorithms can do well too. In Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA '22, pages 411-417, New York, NY, USA, 2022. Association for Computing Machinery. URL: https://doi.org/10.1145/3490148.3538580.
  10. Matej Lieskovský and Jiří Sgall. Graph burning and non-uniform k-centers for small treewidth. In Parinya Chalermsook and Bundit Laekhanukit, editors, Approximation and Online Algorithms, pages 20-35, Cham, 2022. Springer International Publishing. Google Scholar
  11. Matej Lieskovský, Jiří Sgall, and Andreas Emil Feldmann. Approximation Algorithms and Lower Bounds for Graph Burning. In Nicole Megow and Adam Smith, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023), volume 275 of Leibniz International Proceedings in Informatics (LIPIcs), pages 9:1-9:17, Dagstuhl, Germany, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.9.
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