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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 As Get 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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