Exploring Temporal Graphs with Frequent and Regular Edges
Duncan Adamson

TL;DR
This paper investigates exploration strategies for two classes of temporal graphs—frequent and regular edges—demonstrating efficient exploration algorithms and analyzing their application to real-world networks like public transport systems.
Contribution
It introduces exploration algorithms for temporal graphs with frequent and regular edges, providing bounds on exploration time and applying these results to practical network models.
Findings
Graphs with frequent edges can be explored in O(F n) timesteps.
Graphs with regular edges can be explored in O(R n) timesteps.
Application to public transport and broadcast networks demonstrates practical relevance.
Abstract
Temporal graphs are a class of graphs defined by a constant set of vertices and a changing set of edges, each of which is known as a timestep. These graphs are well motivated in modelling real-world networks, where connections may change over time. One such example, itself the primary motivation for this paper, are public transport networks, where vertices represent stops and edges the connections available at some given time. Exploration problems are one of the most studied problems for temporal graphs, asking if an agent starting at some given vertex can visit every vertex in the graph. In this paper, we study two primary classes of temporal graphs. First, we study temporal graphs with \emph{frequent edges}, temporal graphs where each edge is active at least once every timesteps, called the frequency of the edge. Second, temporal graphs with \emph{regular edges},…
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Taxonomy
TopicsConstraint Satisfaction and Optimization · Data Management and Algorithms
