Faster Exploration of Some Temporal Graphs
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.
Temporal Graphs
Graph Exploration
Mathematics of computing~Paths and connectivity problems
5:1-5:10
Regular Paper
Duncan
Adamson
Duncan Adamson
Department of Computer Science, Reykjavik University, Iceland
Funded by the Leverhulme trust.
Vladimir V.
Gusev
Vladimir V. Gusev
Materials Innovation Factory, University of Liverpool, UK
Department of Computer Science, University of Liverpool
funded by the Leverhulme trust.
Dmitriy
Malyshev
Dmitriy Malyshev
Laboratory of Algorithms and Technologies for Network Analysis, HSE University, Nizhny Novgorod, Russian Federation
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).
Viktor
Zamaraev
Viktor Zamaraev
Department of Computer Science, University of Liverpool, UK
10.4230/LIPIcs.SAND.2022.5
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Duncan Adamson, Vladimir V. Gusev, Dmitriy Malyshev, and Viktor Zamaraev
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