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Brief Announcement

DOI: 10.4230/LIPIcs.SAND.2025.18

Brief Announcement: The Shortest Temporal Exploration Problem

Authors: Stefan Balev, Éric Sanlaville, and Antoine Toullalan

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract

A temporal graph is a graph for which the edge set can change from one time step to the next. This paper considers undirected temporal graphs defined over L time steps and connected at each time step. We study the Shortest Temporal Exploration Problem (STEXP) that, given the evolution of the graph, asks for a temporal walk that starts at a given vertex, moves over at most one edge at each time step, visits all the vertices, takes at most L time steps and traverses the smallest number of edges. We prove that every constantly connected temporal graph with n vertices can be explored with O(n^{1.5}) edges traversed if L is O(n^{3.5}) time steps. This result improves the upper bound of O(n²) edges when L is Ω(n²). Moreover, we study the case where the graph has a diameter bounded by a parameter k at each time step and we prove that there exists an exploration which takes O(kn²) time steps and traverses O(kn) edges. Finally, the case where the underlying graph is a cycle is studied and tight linear bounds are provided on the number of edges traversed in the worst-case.

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Stefan Balev, Éric Sanlaville, and Antoine Toullalan. Brief Announcement: The Shortest Temporal Exploration Problem. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 18:1-18:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balev_et_al:LIPIcs.SAND.2025.18,
  author =	{Balev, Stefan and Sanlaville, \'{E}ric and Toullalan, Antoine},
  title =	{{Brief Announcement: The Shortest Temporal Exploration Problem}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{18:1--18:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.18},
  URN =		{urn:nbn:de:0030-drops-230716},
  doi =		{10.4230/LIPIcs.SAND.2025.18},
  annote =	{Keywords: Graph Theory, Temporal Graph, Temporal Graph Exploration}
}

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Brief Announcement: The Shortest Temporal Exploration Problem

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