Improved exploration of temporal graphs
Paul Bastide, Carla Groenland, Lukas Michel, Cl\'ement Rambaud

TL;DR
This paper improves the upper bounds on the time needed to explore temporal graphs, especially when the underlying graphs are connected with bounded average degree, by introducing a more general and efficient approach.
Contribution
It presents a significantly improved bound for temporal exploration, extending previous results to cases with bounded average degree and unifying various graph classes.
Findings
Achieves exploration in 3f3(n^{3/2} \u221a{\,D \, ext{log} n}) time for connected graphs.
Provides the first subquadratic bound for graphs with bounded average degree.
Unifies exploration bounds for planar, bounded treewidth, and other graph classes.
Abstract
A temporal graph is a sequence of graphs on the same vertex set of size . The \emph{temporal exploration problem} asks for the length of the shortest sequence of vertices that starts at a given vertex, visits every vertex, and at each time step either stays at the current vertex or moves to an adjacent vertex in . Bounds on the length of a shortest temporal exploration have been investigated extensively. Perhaps the most fundamental case is when each graph is connected and has bounded maximum degree. In this setting, Erlebach, Kammer, Luo, Sajenko, and Spooner [ICALP 2019] showed that there exists an exploration of in time steps. We significantly improve this bound by showing that time steps suffice. In fact, we deduce this result from a much more general statement. Let the…
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Taxonomy
TopicsOpportunistic and Delay-Tolerant Networks · Optimization and Search Problems · Computational Geometry and Mesh Generation
