Delay-Robust Routes in Temporal Graphs

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

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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). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 30:1-30:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Most transportation networks are inherently temporal: Connections (e.g. flights, train runs) are only available at certain, scheduled times. When transporting passengers or commodities, this fact must be considered for the the planning of itineraries. This has already led to several well-studied algorithmic problems on temporal graphs. The difficulty of the described task is increased by the fact that connections are often unreliable - in particular, many modes of transportation suffer from occasional delays. If these delays cause subsequent connections to be missed, the consequences can be severe. Thus, it is a vital problem to design itineraries that are robust to (small) delays. We initiate the study of this problem from a parameterized complexity perspective by proving its NP-completeness as well as several hardness and tractability results for natural parameterizations.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Fixed parameter tractability
  • Mathematics of computing → Discrete mathematics
  • algorithms and complexity
  • parameterized complexity
  • time-varying networks
  • temporal paths
  • journeys


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  1. 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:
  2. Kenneth A Berman. Vulnerability of scheduled networks and a generalization of Menger’s theorem. Networks, 28(3):125-134, 1996. URL:<125::AID-NET1>3.0.CO;2-P.
  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:
  4. Sebastian Buß, Hendrik Molter, Rolf Niedermeier, and Maciej Rymar. Algorithmic aspects of temporal betweenness. In Proceedings of the 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2020, pages 2084-2092. ACM, 2020. URL:
  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:
  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:
  7. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. URL:
  8. 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:
  9. Edsger W Dijkstra et al. A note on two problems in connexion with graphs. Numerische Mathematik, 1(1):269-271, 1959. URL:
  10. Rodney G. Downey and Michael R. Fellows. Fundamentals of Parameterized Complexity. Springer, 2013. URL:
  11. Jessica Enright and Kitty Meeks. Deleting edges to restrict the size of an epidemic: a new application for treewidth. Algorithmica, 80(6):1857-1889, 2018. URL:
  12. 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:
  13. 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:
  14. Thomas Erlebach, Michael Hoffmann, and Frank Kammer. On temporal graph exploration. Journal of Computer and System Sciences, 119:1-18, 2021. URL:
  15. Michael R Fellows, Danny Hermelin, Frances Rosamond, and Stéphane Vialette. On the parameterized complexity of multiple-interval graph problems. Theoretical Computer Science, 410(1):53-61, 2009. URL:
  16. 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:
  17. Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken. Delay-robust routes in temporal graphs, 2022. URL:
  18. Eugen Füchsle, Hendrik Molter, Rolf Niedermeier, and Malte Renken. Temporal connectivity: Coping with foreseen and unforeseen delays, 2022. URL:
  19. Petter Holme. Modern temporal network theory: a colloquium. The European Physical Journal B, 88(9):234, 2015. URL:
  20. Petter Holme and Jari Saramäki, editors. Temporal Network Theory. Springer, 2019. URL:
  21. Richard M Karp. Reducibility among combinatorial problems, pages 85-103. Springer, 1972. URL:
  22. 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:
  23. Nina Klobas, George B. Mertzios, Hendrik Molter, Rolf Niedermeier, and Philipp Zschoche. Interference-free walks in time: Temporally disjoint paths. In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, pages 4090-4096., 2021. URL:
  24. 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:
  25. Othon Michail. An introduction to temporal graphs: An algorithmic perspective. Internet Mathematics, 12(4):239-280, 2016. URL:
  26. 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:
  27. Manuel Sorge and Mathias Weller. The graph parameter hierarchy. unpublished manuscript, 2019. URL:
  28. 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:
  29. 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:
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