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Graph Burning and Non-uniform k-centers for Small Treewidth

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Approximation and Online Algorithms (WAOA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13538))

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Abstract

We study the graph burning problem and give a polynomial-time approximation scheme (PTAS) for arbitrary graphs of constant treewidth. This significantly extends the previous results, as a PTAS was known only for disjoint union of paths.

As a building block, we give an algorithm that proves the non-uniform k-center problem to be in XP when parameterized by the number of different radii and the treewidth of the graph. This extends the known exactly solvable cases of the non-uniform k-center problem; in particular this also solves the k-center with outliers on graphs of small treewidth exactly.

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Acknowledgements

Partially supported by project SVV-2020-260578 and GA ČR project 19-27871X. We are grateful to anonymous referees for many helpful comments and references.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Computer Science Institute of Charles University, Prague, Czechia

    Matej Lieskovský & Jiří Sgall

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  1. Matej Lieskovský
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  2. Jiří Sgall
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Correspondence to Jiří Sgall .

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Editors and Affiliations

  1. Aalto University, Espoo, Finland

    Parinya Chalermsook

  2. Shanghai University of Finance and Economics, Shanghai, China

    Bundit Laekhanukit

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Lieskovský, M., Sgall, J. (2022). Graph Burning and Non-uniform k-centers for Small Treewidth. In: Chalermsook, P., Laekhanukit, B. (eds) Approximation and Online Algorithms. WAOA 2022. Lecture Notes in Computer Science, vol 13538. Springer, Cham. https://doi.org/10.1007/978-3-031-18367-6_2

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  • DOI: https://doi.org/10.1007/978-3-031-18367-6_2

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  • Online ISBN: 978-3-031-18367-6

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