Faster exploration of some temporal graphs
Date
29/04/2022Metadata
Show full item recordAbstract
A temporal graph G = (G1, G2,..., GT ) is a graph represented by a sequence of T graphs over a common set of vertices, such that at the ith time step only the edge set Ei 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(kn1.5 log n) days if the underlying graph has treewidth k and in O(n1.75 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.
Citation
Adamson , D , Gusev , V V , Malyshev , D & Zamaraev , V 2022 , Faster exploration of some temporal graphs . in J Aspnes & O Michail (eds) , 1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022 . , 5 , Leibniz International Proceedings in Informatics, LIPIcs , vol. 221 , Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing , 1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022 , Virtual, Online , 28/03/22 . https://doi.org/10.4230/LIPIcs.SAND.2022.5 conference
Publication
1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022
ISSN
1868-8969Type
Conference item
Description
Funding Adamson, Duncan: Funded by the Leverhulme trust. Gusev, Vladimir V.: funded by the Leverhulme trust. Malyshev, Dmitriy: The work of Dmitriy Malyshev was conducted within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE).Collections
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