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Temporal Connectivity: Coping with Foreseen and Unforeseen Delays

Authors Eugen Füchsle, Hendrik Molter , Rolf Niedermeier , Malte Renken

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Author Details

Eugen Füchsle
  • Faculty IV, Algorithmics and Computational Complexity, TU Berlin, Germany
Hendrik Molter
  • Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Rolf Niedermeier
  • Faculty IV, Algorithmics and Computational Complexity, TU Berlin, Germany
Malte Renken
  • Faculty IV, Algorithmics and Computational Complexity, TU Berlin, Germany

Funding

  • Molter, Hendrik: Supported by the ISF, grant No. 1070/20.
  • Renken, Malte: Supported by the DFG, project MATE (NI 369/17).

Cite AsGet BibTex

Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken. Temporal Connectivity: Coping with Foreseen and Unforeseen Delays. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.SAND.2022.17

Abstract

Consider planning a trip in a train network. In contrast to, say, a road network, the edges are temporal, i.e., they are only available at certain times. Another important difficulty is that trains, unfortunately, sometimes get delayed. This is especially bad if it causes one to miss subsequent trains. The best way to prepare against this is to have a connection that is robust to some number of (small) delays. An important factor in determining the robustness of a connection is how far in advance delays are announced. We give polynomial-time algorithms for the two extreme cases: delays known before departure and delays occurring without prior warning (the latter leading to a two-player game scenario). Interestingly, in the latter case, we show that the problem becomes PSPACE-complete if the itinerary is demanded to be a path.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Problems, reductions and completeness
  • Mathematics of computing → Discrete mathematics
Keywords
  • Paths and walks in temporal graphs
  • static expansions of temporal graphs
  • two-player games
  • flow computations
  • dynamic programming
  • PSPACE-completeness

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References

  1. Sanjeev Arora and Boaz Barak. Computational Complexity: A Modern Approach. Cambridge University Press, 2009. Google Scholar
  2. Matthias Bentert, Anne-Sophie Himmel, André Nichterlein, and Rolf Niedermeier. Efficient computation of optimal temporal walks under waiting-time constraints. Applied Network Science, 5(1):73, 2020. URL: https://doi.org/10.1007/s41109-020-00311-0.
  3. Binh-Minh Bui-Xuan, Afonso Ferreira, and Aubin Jarry. Computing shortest, fastest, and foremost journeys in dynamic networks. International Journal of Foundations of Computer Science, 14(02):267-285, 2003. URL: https://doi.org/10.1142/S0129054103001728.
  4. Sebastian Buß, Hendrik Molter, Rolf Niedermeier, and Maciej Rymar. Algorithmic aspects of temporal betweenness. In Proceedings of the 26th SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), pages 2084-2092, 2020. URL: https://doi.org/10.1145/3394486.3403259.
  5. Arnaud Casteigts, Paola Flocchini, Walter Quattrociocchi, and Nicola Santoro. Time-varying graphs and dynamic networks. International Journal of Parallel, Emergent and Distributed Systems, 27(5):387-408, 2012. URL: https://doi.org/10.1080/17445760.2012.668546.
  6. 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.
  7. Argyrios Deligkas and Igor Potapov. Optimizing reachability sets in temporal graphs by delaying. In Proceedings of the 34th Conference on Artificial Intelligence (AAAI), pages 9810-9817, 2020. URL: https://doi.org/10.1609/aaai.v34i06.6533.
  8. Peter Elias, Amiel Feinstein, and Claude E. Shannon. A note on the maximum flow through a network. IRE Transactions on Information Theory, 2(4):117-119, 1956. URL: https://doi.org/10.1109/TIT.1956.1056816.
  9. Jessica Enright, Kitty Meeks, George B. Mertzios, and Viktor Zamaraev. Deleting edges to restrict the size of an epidemic in temporal networks. Journal of Computer and System Sciences, 119:60-77, 2021. URL: https://doi.org/10.1016/j.jcss.2021.01.007.
  10. Jessica Enright, Kitty Meeks, and Fiona Skerman. Assigning times to minimise reachability in temporal graphs. Journal of Computer and System Sciences, 115:169-186, 2021. URL: https://doi.org/10.1016/j.jcss.2020.08.001.
  11. Thomas Erlebach, Michael Hoffmann, and Frank Kammer. On temporal graph exploration. Journal of Computer and System Sciences, 119:1-18, 2021. URL: https://doi.org/10.1016/j.jcss.2021.01.005.
  12. Till Fluschnik, Hendrik Molter, Rolf Niedermeier, Malte Renken, and Philipp Zschoche. Temporal graph classes: A view through temporal separators. Theoretical Computer Science, 806:197-218, 2020. URL: https://doi.org/10.1016/j.tcs.2019.03.031.
  13. L. R. Ford and D. R. Fulkerson. Maximal flow through a network. Canadian Journal of Mathematics, 8:399-404, 1956. URL: https://doi.org/10.4153/CJM-1956-045-5.
  14. Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken. Delay-robust routes in temporal graphs. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022), volume 219 of Leibniz International Proceedings in Informatics (LIPIcs), pages 30:1-30:15, 2022. URL: https://doi.org/10.4230/LIPIcs.STACS.2022.30.
  15. Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken. Temporal connectivity: Coping with foreseen and unforeseen delays, 2022. URL: http://arxiv.org/abs/2201.05011.
  16. Petter Holme. Modern temporal network theory: a colloquium. The European Physical Journal B, 88(9):234, 2015. URL: https://doi.org/10.1140/epjb/e2015-60657-4.
  17. Petter Holme and Jari Saramäki, editors. Temporal Network Theory. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-23495-9.
  18. David Kempe, Jon Kleinberg, and Amit Kumar. Connectivity and inference problems for temporal networks. Journal of Computer and System Sciences, 64(4):820-842, 2002. URL: https://doi.org/10.1006/jcss.2002.1829.
  19. Nina Klobas, George B. Mertzios, Hendrik Molter, Rolf Niedermeier, and Philipp Zschoche. Interference-free walks in time: Temporally disjoint paths. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI), pages 4090-4096, 2021. URL: https://doi.org/10.24963/ijcai.2021/563.
  20. Matthieu Latapy, Tiphaine Viard, and Clémence Magnien. Stream graphs and link streams for the modeling of interactions over time. Social Network Analysis and Mining, 8(1):61, 2018. URL: https://doi.org/10.1007/s13278-018-0537-7.
  21. George B Mertzios, Othon Michail, and Paul G Spirakis. Temporal network optimization subject to connectivity constraints. Algorithmica, 81(4):1416-1449, 2019. URL: https://doi.org/10.1007/s00453-018-0478-6.
  22. Hendrik Molter, Malte Renken, and Philipp Zschoche. Temporal reachability minimization: Delaying vs. deleting. In Proceedings of the 46th International Symposium on Mathematical Foundations of Computer Science (MFCS), pages 76:1-76:15, 2021. URL: https://doi.org/10.4230/LIPIcs.MFCS.2021.76.
  23. Amir Afrasiabi Rad, Paola Flocchini, and Joanne Gaudet. Computation and analysis of temporal betweenness in a knowledge mobilization network. Computational Social Networks, 4(1):1-22, 2017. URL: https://doi.org/10.1186/s40649-017-0041-7.
  24. Maciej Rymar, Hendrik Molter, André Nichterlein, and Rolf Niedermeier. Towards classifying the polynomial-time solvability of temporal betweenness centrality. In Proceedings of the 47th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), pages 219-231, 2021. URL: https://doi.org/10.1007/978-3-030-86838-3_17.
  25. Aaron N. Siegel. Combinatorial game theory. American Mathematical Society, 2013. Google Scholar
  26. Huanhuan Wu, James Cheng, Yiping Ke, Silu Huang, Yuzhen Huang, and Hejun Wu. Efficient algorithms for temporal path computation. IEEE Transactions on Knowledge and Data Engineering, 28(11):2927-2942, 2016. URL: https://doi.org/10.1109/TKDE.2016.2594065.
  27. Philipp Zschoche, Till Fluschnik, Hendrik Molter, and Rolf Niedermeier. The complexity of finding small separators in temporal graphs. Journal of Computer and System Sciences, 107:72-92, 2020. URL: https://doi.org/10.1016/j.jcss.2019.07.006.
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