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.2022.7
URN: urn:nbn:de:0030-drops-171299
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17129/
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Mehta, Hermish ; Reichman, Daniel

Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks

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LIPIcs-APPROX7.pdf (0.6 MB)

Abstract

We study the notion of local treewidth in sparse random graphs: the maximum treewidth over all k-vertex subgraphs of an n-vertex graph. When k is not too large, we give nearly tight bounds for this local treewidth parameter; we also derive nearly tight bounds for the local treewidth of noisy trees, trees where every non-edge is added independently with small probability. We apply our upper bounds on the local treewidth to obtain fixed parameter tractable algorithms (on random graphs and noisy trees) for edge-removal problems centered around containing a contagious process evolving over a network. In these problems, our main parameter of study is k, the number of initially "infected" vertices in the network. For the random graph models we consider and a certain range of parameters the running time of our algorithms on n-vertex graphs is 2^o(k) poly(n), improving upon the 2^Ω(k) poly(n) performance of the best-known algorithms designed for worst-case instances of these edge deletion problems.

BibTeX - Entry

@InProceedings{mehta_et_al:LIPIcs.APPROX/RANDOM.2022.7,
  author =	{Mehta, Hermish and Reichman, Daniel},
  title =	{{Local Treewidth of Random and Noisy Graphs with Applications to Stopping Contagion in Networks}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17129},
  URN =		{urn:nbn:de:0030-drops-171299},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.7},
  annote =	{Keywords: Graph Algorithms, Random Graphs, Data Structures and Algorithms, Discrete Mathematics}
}

Keywords: Graph Algorithms, Random Graphs, Data Structures and Algorithms, Discrete Mathematics
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)
Issue Date: 2022
Date of publication: 15.09.2022

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