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.SAND.2022.5
URN: urn:nbn:de:0030-drops-159475
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15947/
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Adamson, Duncan ; Gusev, Vladimir V. ; Malyshev, Dmitriy ; Zamaraev, Viktor

Faster Exploration of Some Temporal Graphs

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LIPIcs-SAND-2022-5.pdf (0.6 MB)

Abstract

A temporal graph G = (G_1, G_2, ..., G_T) is a graph represented by a sequence of T graphs over a common set of vertices, such that at the i-th time step only the edge set E_i is active. The temporal graph exploration problem asks for a shortest temporal walk on some temporal graph visiting every vertex. We show that temporal graphs with n vertices can be explored in O(k n^{1.5} log n) days if the underlying graph has treewidth k and in O(n^{1.75} log n) days if the underlying graph is planar. Furthermore, we show that any temporal graph whose underlying graph is a cycle with k chords can be explored in at most 6kn days. Finally, we demonstrate that there are temporal realisations of sub cubic planar graphs that cannot be explored faster than in Ω(n log n) days. All these improve best known results in the literature.

BibTeX - Entry

@InProceedings{adamson_et_al:LIPIcs.SAND.2022.5,
  author =	{Adamson, Duncan and Gusev, Vladimir V. and Malyshev, Dmitriy and Zamaraev, Viktor},
  title =	{{Faster Exploration of Some Temporal Graphs}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{5:1--5:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15947},
  URN =		{urn:nbn:de:0030-drops-159475},
  doi =		{10.4230/LIPIcs.SAND.2022.5},
  annote =	{Keywords: Temporal Graphs, Graph Exploration}
}

Keywords: Temporal Graphs, Graph Exploration
Collection: 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)
Issue Date: 2022
Date of publication: 29.04.2022

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