License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.9
URN: urn:nbn:de:0030-drops-188345
URL: https://drops.dagstuhl.de/opus/volltexte/2023/18834/
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Lieskovský, Matej ; Sgall, Jiří ; Feldmann, Andreas Emil

Approximation Algorithms and Lower Bounds for Graph Burning

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LIPIcs-APPROX9.pdf (0.8 MB)


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.

BibTeX - Entry

@InProceedings{lieskovsky_et_al:LIPIcs.APPROX/RANDOM.2023.9,
  author =	{Lieskovsk\'{y}, Matej and Sgall, Ji\v{r}{\'\i} and Feldmann, Andreas Emil},
  title =	{{Approximation Algorithms and Lower Bounds for Graph Burning}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18834},
  URN =		{urn:nbn:de:0030-drops-188345},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.9},
  annote =	{Keywords: Graph Algorithms, approximation Algorithms, randomized Algorithms}
}

Keywords: Graph Algorithms, approximation Algorithms, randomized Algorithms
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)
Issue Date: 2023
Date of publication: 04.09.2023


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