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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18834/
Lieskovský, Matej ;
Sgall, Jiří ;
Feldmann, Andreas Emil
Approximation Algorithms and Lower Bounds for Graph Burning
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: |
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Graph Algorithms, approximation Algorithms, randomized Algorithms |
Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) |
Issue Date: |
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2023 |
Date of publication: |
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04.09.2023 |