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Online Space-Time Travel Planning in Dynamic Graphs

Authors Quentin Bramas , Jean-Romain Luttringer , Sébastien Tixeuil

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Author Details

Quentin Bramas
  • University of Strasbourg, ICUBE, CNRS, Strasbourg, France
Jean-Romain Luttringer
  • University of Strasbourg, ICUBE, CNRS, Strasbourg, France
Sébastien Tixeuil
  • Sorbonne University, CNRS, LIP6, Institut Universitaire de France, Paris, France

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Quentin Bramas, Jean-Romain Luttringer, and Sébastien Tixeuil. Online Space-Time Travel Planning in Dynamic Graphs. In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, pp. 7:1-7:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.SAND.2024.7

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Dynamic graphs
  • online algorithm
  • space-time travel
  • treasure hunt

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References

  1. Adri Bhattacharya, Barun Gorain, and Partha Sarathi Mandal. Treasure hunt in graph using pebbles. In International Symposium on Stabilizing, Safety, and Security of Distributed Systems, pages 99-113. Springer, 2022. Google Scholar
  2. Alexander Birx, Yann Disser, Alexander V Hopp, and Christina Karousatou. An improved lower bound for competitive graph exploration. Theoretical Computer Science, 868:65-86, 2021. Google Scholar
  3. Sébastien Bouchard, Yoann Dieudonné, Arnaud Labourel, and Andrzej Pelc. Almost-optimal deterministic treasure hunt in unweighted graphs. ACM Transactions on Algorithms, 19(3):1-32, 2023. Google Scholar
  4. Quentin Bramas, Jean-Romain Luttringer, and Sébastien Tixeuil. Offline constrained backward time travel planning. In Shlomi Dolev and Baruch Schieber, editors, Stabilization, Safety, and Security of Distributed Systems - 25th International Symposium, SSS 2023, Jersey City, NJ, USA, October 2-4, 2023, Proceedings, volume 14310 of Lecture Notes in Computer Science, pages 466-480. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-44274-2_35.
  5. Sebastian Brandt, Klaus-Tycho Foerster, Jonathan Maurer, and Roger Wattenhofer. Online graph exploration on a restricted graph class: Optimal solutions for tadpole graphs. Theoretical Computer Science, 839:176-185, 2020. Google Scholar
  6. Arnaud Casteigts, Paola Flocchini, Bernard Mans, and Nicola Santoro. Shortest, fastest, and foremost broadcast in dynamic networks. Int. J. Found. Comput. Sci., 26(4):499-522, 2015. URL: https://doi.org/10.1142/S0129054115500288.
  7. Arnaud Casteigts, Paola Flocchini, Walter Quattrociocchi, and Nicola Santoro. Time-varying graphs and dynamic networks. Int. J. Parallel Emergent Distributed Syst., 27(5):387-408, 2012. URL: https://doi.org/10.1080/17445760.2012.668546.
  8. Arnaud Casteigts, Anne-Sophie Himmel, Hendrik Molter, and Philipp Zschoche. Finding temporal paths under waiting time constraints. Algorithmica, 83(9):2754-2802, 2021. URL: https://doi.org/10.1007/s00453-021-00831-w.
  9. Arnaud Casteigts, Joseph G. Peters, and Jason Schoeters. Temporal cliques admit sparse spanners. J. Comput. Syst. Sci., 121:1-17, 2021. URL: https://doi.org/10.1016/j.jcss.2021.04.004.
  10. Shigang Chen and Klara Nahrstedt. An overview of qos routing for the next generation high-speed networks: Problems and solutions. Network, IEEE, 12:64-79, December 1998. URL: https://doi.org/10.1109/65.752646.
  11. Dariusz Dereniowski, Yann Disser, Adrian Kosowski, Dominik Pająk, and Przemysław Uznański. Fast collaborative graph exploration. Information and Computation, 243:37-49, 2015. Google Scholar
  12. Yann Disser, Frank Mousset, Andreas Noever, Nemanja Škorić, and Angelika Steger. A general lower bound for collaborative tree exploration. Theoretical Computer Science, 811:70-78, 2020. Google Scholar
  13. Afonso Ferreira. On models and algorithms for dynamic communication networks: The case for evolving graphs. In Quatrièmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications (ALGOTEL 2002), pages 155-161, Mèze, France, May 2002. INRIA Press. Google Scholar
  14. Klaus-Tycho Foerster and Roger Wattenhofer. Lower and upper competitive bounds for online directed graph exploration. Theoretical Computer Science, 655:15-29, 2016. Google Scholar
  15. Robin Fritsch. Online graph exploration on trees, unicyclic graphs and cactus graphs. Information Processing Letters, 168:106096, 2021. Google Scholar
  16. Rosario G. Garroppo, Stefano Giordano, and Luca Tavanti. A survey on multi-constrained optimal path computation: Exact and approximate algorithms. Computer Networks, 54(17):3081-3107, December 2010. URL: https://doi.org/10.1016/j.comnet.2010.05.017.
  17. Jochen W. Guck, Amaury Van Bemten, Martin Reisslein, and Wolfgang Kellerer. Unicast qos routing algorithms for sdn: A comprehensive survey and performance evaluation. IEEE Communications Surveys & Tutorials, 20(1):388-415, 2018. URL: https://doi.org/10.1109/COMST.2017.2749760.
  18. Dennis Komm, Rastislav Královič, Richard Královič, and Jasmin Smula. Treasure hunt with advice. In Christian Scheideler, editor, Structural Information and Communication Complexity, pages 328-341, Cham, 2015. Springer International Publishing. Google Scholar
  19. Giuseppe Antonio Di Luna, Paola Flocchini, Giuseppe Prencipe, and Nicola Santoro. Black hole search in dynamic rings. In 41st IEEE International Conference on Distributed Computing Systems, ICDCS 2021, Washington DC, USA, July 7-10, 2021, pages 987-997. IEEE, 2021. URL: https://doi.org/10.1109/ICDCS51616.2021.00098.
  20. Juan Villacis-Llobet, Binh-Minh Bui-Xuan, and Maria Potop-Butucaru. Foremost non-stop journey arrival in linear time. In Merav Parter, editor, Structural Information and Communication Complexity - 29th International Colloquium, SIROCCO 2022, Paderborn, Germany, June 27-29, 2022, Proceedings, volume 13298 of Lecture Notes in Computer Science, pages 283-301. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-09993-9_16.
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