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Multi-criteria Shortest Paths in Time-Dependent Train Networks

  • Yann Disser
  • Matthias Müller–Hannemann
  • Mathias Schnee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5038)

Abstract

We study the problem of finding all Pareto-optimal solutions in a multi-criteria setting of the shortest path problem in time-dependent graphs. This has important applications in timetable information systems for train schedules. We present a new prototype to solve this problem in a fully realistic scenario based on a multi-criteria generalization of Dijkstra’s algorithm. As optimization criteria we use travel time and number of train changes, as well as a new criterion “reliability of transfers”.

The performance of the prototype and various speed-up techniques are analyzed experimentally on a large set of real test instances. In comparison with a base-line implementation, our prototype achieves significant speed-up factors of 20 with respect to the number of label creations and of 138 with respect to label insertions into the priority queue. We also compare our prototype with a time-expanded graph model.

Keywords

shortest paths time-dependent graphs multi-criteria optimization speed-up techniques case study 

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References

  1. 1.
  2. 2.
    Müller-Hannemann, M., Weihe, K.: On the cardinality of the Pareto set in bicriteria shortest path problems. Annals of Operations Research 147, 269–286 (2006)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Pallottino, S., Scutellà, M.G.: Shortest path algorithms in transportation models: Classical and innovative aspects. In: Equilibrium and Advanced Transportation Modelling, Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  4. 4.
    Schulz, F., Wagner, D., Weihe, K.: Dijkstra’s algorithm on-line: An empirical case study from public railroad transport. ACM Journal of Experimental Algorithmics, Article 12, 5 (2000)Google Scholar
  5. 5.
    Pyrga, E., Schulz, F., Wagner, D., Zaroliagis, C.: Efficient models for timetable information in public transportation systems. ACM Journal of Experimental Algorithmics (JEA) 12, 2.4 (2007)MathSciNetGoogle Scholar
  6. 6.
    Cooke, K.L., Halsey, E.: The shortest route through a network with time-dependent internodal transit times. Journal of Mathematical Analysis and Applications 14, 493–498 (1966)CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. Journal of the ACM 37, 607–625 (1990)CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Orda, A., Rom, R.: Minimum weight paths in time-dependent networks. Networks 21, 295–319 (1991)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Nachtigal, K.: Time depending shortest-path problems with applications to railway networks. European Journal of Operations Research 83, 154–166 (1995)CrossRefGoogle Scholar
  10. 10.
    Brodal, G.S., Jacob, R.: Time-dependent networks as models to achieve fast exact time-table queries. In: Proceedings of the 3rd Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS 2003). Electronic Notes in Theoretical Computer Science, vol. 92, pp. 3–15. Elsevier, Amsterdam (2004)Google Scholar
  11. 11.
    Pyrga, E., Schulz, F., Wagner, D., Zaroliagis, C.: Towards realistic modeling of time-table information through the time-dependent approach. In: Proceedings of the 3rd Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS 2003). Electronic Notes in Theoretical Computer Science, vol. 92, pp. 85–103. Elsevier, Amsterdam (2004)Google Scholar
  12. 12.
    Müller-Hannemann, M., Schulz, F., Wagner, D., Zaroliagis, C.: Timetable information: Models and algorithms. In: Geraets, F., Kroon, L.G., Schoebel, A., Wagner, D., Zaroliagis, C.D. (eds.) Railway Optimization 2004. LNCS, vol. 4359, pp. 67–89. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Müller-Hannemann, M., Schnee, M.: Finding all attractive train connections by multi-criteria Pareto search. In: Geraets, F., Kroon, L.G., Schoebel, A., Wagner, D., Zaroliagis, C.D. (eds.) Railway Optimization 2004. LNCS, vol. 4359, pp. 246–263. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Bauer, R., Delling, D., Wagner, D.: Experimental study on speed-up techniques for timetable information systems. In: ATMOS 2007 (2007)Google Scholar
  15. 15.
    Bauer, R., Delling, D.: SHARC: Fast and Robust Unidirectional Routing. In: Proceedings of the 9th Workshop on Algorithm Engineering and Experiments (ALENEX 2008) (2008)Google Scholar
  16. 16.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)CrossRefMathSciNetzbMATHGoogle Scholar
  17. 17.
    Möhring, R.H.: Verteilte Verbindungssuche im öffentlichen Personenverkehr: Graphentheoretische Modelle und Algorithmen. In: Angewandte Mathematik - insbesondere Informatik, Vieweg, pp. 192–220 (1999)Google Scholar
  18. 18.
    Theune, D.: Robuste und effiziente Methoden zur Lösung von Wegproblemen. Teubner Verlag, Stuttgart (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yann Disser
    • 1
  • Matthias Müller–Hannemann
    • 2
  • Mathias Schnee
    • 1
  1. 1.Department of Computer ScienceTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of Computer ScienceMartin-Luther-Universität Halle-WittenbergHalleGermany

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