Online Space-Time Travel Planning in Dynamic Graphs - Ecole Nationale du Génie de l'Eau et de l'Environnement de Strasbourg
Communication Dans Un Congrès Année : 2024

Online Space-Time Travel Planning in Dynamic Graphs

Résumé

We study the problem of traveling in an unknown dynamic graph, to reach a destination with minimum latency. At each step of the execution, an agent can decide to move to a neighboring node if an edge exists at this time instant, wait at the current node in the hope that other links will appear in the future, or move backward in time using an expensive time travel device. A travel that makes use of backward time travel is called a space-time travel. Our aim is to arrive at the destination with zero delay, which always requires the use of backward time travel if no path exists to the destination during the first time instant. Finding an optimal space-time travel is polynomial when the agent knows the entire dynamic graph (including the future edges), even with additional constraints. However, we consider in this paper that the agent discovers the dynamic graph while it is exploring it, in an online manner. In this paper, we propose two models that define how an agent learns new knowledge about the dynamic graph during the execution of its protocol: the T-online model, where the agent reaching time t learns about the entire past of the network until t (even nodes not yet visited), and the S-online model, where the agent learns about the past and future about the current node he is located at. We present an algorithm with an optimal competitive ratio of 2 for the T-online model. In the S-online model, we prove a lower bound of 2/3n − 7/4 and an upper bound of 2n − 3 on the optimal competitive ratio when the cost function is linear.
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Dates et versions

hal-04622850 , version 1 (24-06-2024)

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Quentin Bramas, Jean-Romain Luttringer, Sébastien Tixeuil. Online Space-Time Travel Planning in Dynamic Graphs. 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024), Jun 2024, Patras, Greece. pp.7:1-7:14, ⟨10.4230/LIPIcs.SAND.2024.7⟩. ⟨hal-04622850⟩
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