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Timetable Information: Models and Algorithms

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Algorithmic Methods for Railway Optimization

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4359))

Abstract

We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transform the problems into shortest path problems are reviewed, including issues like the modeling of realistic details (e.g., train transfers) and further optimization criteria (e.g., the number of transfers). An important topic is also multi-criteria optimization, where in general all attractive connections with respect to several criteria shall be determined. Finally, we discuss the performance of the described algorithms, which is crucial for their application in a real system.

Partially supported by the Future and Emerging Technologies Unit of EC (IST priority - 6th FP), under contract no. FP6-021235-2 (project ARRIVAL).

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References

  1. Ackermann, H., Newman, A., Röglin, H., Vöcking, B.: Decision making based on approximate and smoothed pareto curves. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 675–684. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Baumann, N., Schmidt, R.: Buxtehude–Garmisch in 6 Sekunden. Die elektronische Fahrplanauskunft (EFA) der Deutschen Bundesbahn. Die Bundesbahn. Zeitschrift für aktuelle Verkehrsfragen, 10, 929–931 (1988)

    Google Scholar 

  3. Brodal, G.S., Jacob, R.: Time-dependent networks as models to achieve fast exact time-table queries. Technical Report ALCOMFT-TR-01-176, BRICS, University of Aarhus, Denmark (2001), http://www.brics.dk/ALCOM-FT/TR/ALCOMFT-TR-01-176.html

  4. 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, Elsevier, Amsterdam (2004), A previous version appeared as [3]

    Google Scholar 

  5. 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)

    Article  MATH  MathSciNet  Google Scholar 

  6. DELFI. Durchgängige elektronische Fahrplaninformation, http://www.delfi.de/

  7. Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  8. EFA. A timetable information system by Mentz Datenverarbeitung GmbH, München, Germany, http://www.mentzdv.de/

  9. Ehrgott, M.: Multicriteria Optimization. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  10. Ehrgott, M., Gandibleux, X.: Multiobjective combinatorial optimization. In: Multiple Criteria Optimization — State of the Art Annotated Bibliographic Surveys, pp. 369–444. Kluwer Academic Publishers, Boston, MA (2002)

    Google Scholar 

  11. EUSpirit. European travel information system, http://www.eu-spirit.com/

  12. Gabriel, S., Bernstein, D.: The traffic equilibrium problem with nonadditive path costs. Transportation Science 31(4), 337–348 (1997)

    Article  MATH  Google Scholar 

  13. HAFAS. A timetable information system by HaCon Ingenieurgesellschaft mbH, Hannover, Germany, http://www.hacon.de/hafas/

  14. Hansen, P.: Bicriteria path problems. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making Theory and Applications. Lecture Notes in Economics and Mathematical Systems, vol. 177, pp. 109–127. Springer, Berlin (1979)

    Google Scholar 

  15. Hensen, D., Truong, T.: Valuation of travel times savings. Journal of Transport Economics and Policy, 237–260 (1985)

    Google Scholar 

  16. Kostreva, M.M., Wiecek, M.M.: Time dependency in multiple objective dynamic programming. Journal of Mathematical Analysis and Applications 173, 289–307 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  17. Loridan, P.: ε-solutions in vector minimization problems. Journal of Optimization Theory and Applications 43, 265–276 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  18. Martins, E.Q.V.: On a multicriteria shortest path problem. European Journal of Operations Research 16, 236–245 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  19. Möhring, R.: Verteilte Verbindungssuche im öffentlichen Personenverkehr: Graphentheoretische Modelle und Algorithmen. In: Angewandte Mathematik – insbesondere Informatik, Vieweg, pp. 192–220 (1999)

    Google Scholar 

  20. Müller-Hannemann, M., Schnee, M.: Finding all attractive train connections by multi-criteria Pareto search. In: Proceedings of the 4th Workshop in Algorithmic Methods and Models for Optimization of Railways (ATMOS 2004), vol. 4359, pp. 246–263 (to appear)

    Google Scholar 

  21. Müller-Hannemann, M., Schnee, M., Weihe, K.: Getting train timetables into the main storage. In: Proceedings of the 2nd Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS 2002). Electronic Notes in Theoretical Computer Science, vol. 66, Elsevier, Amsterdam (2002)

    Google Scholar 

  22. Müller-Hannemann, M., Weihe, K.: Pareto shortest paths is often feasible in practice. In: Brodal, G.S., Frigioni, D., Marchetti-Spaccamela, A. (eds.) WAE 2001. LNCS, vol. 2141, pp. 185–198. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  23. Nachtigal, K.: Time depending shortest-path problems with applications to railway networks. European Journal of Operations Research 83, 154–166 (1995)

    Article  Google Scholar 

  24. Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. Journal of the ACM, 37(3) (1990)

    Google Scholar 

  25. Orda, A., Rom, R.: Minimum weight paths in time-dependent networks. Networks, 21 (1991)

    Google Scholar 

  26. Pallottino, S., Scutellà, M.G.: Shortest path algorithms in transportation models: Classical and innovative aspects. In: Equilibrium and Advanced Transportation Modelling, ch. 11, Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  27. Papadimitriou, C., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources. In: Proc. 41st IEEE Symp. on Foundations of Computer Science – FOCS 2000, pp. 86–92 (2000)

    Google Scholar 

  28. Pyrga, E., Schulz, F., Wagner, D., Zaroliagis, C.: Experimental comparison of shortest path approaches for timetable information. In: Proceedings of the Sixth Workshop on Algorithm Engineering and Experiments, SIAM, pp. 88–99 (2004)

    Google Scholar 

  29. 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 

  30. Pyrga, E., Schulz, F., Wagner, D., Zaroliagis, C.: Efficient Models for Timetable Information in Public Transportation Systems. ACM Journal of Experimental Algorithmics, 12(2.4) (2007)

    Google Scholar 

  31. Rote, G.: Path problems in graphs. In: Tinhofer, G., Mayr, E., Noltemeier, H., Syslo, M. (eds.) Computational Graph Theory, pp. 155–190. Springer, Heidelberg (1990)

    Google Scholar 

  32. Schulz, F.: Timetable Information and Shortest Paths. PhD thesis, Universität Karlsruhe (TH), Fakultät Informatik (2005)

    Google Scholar 

  33. Schulz, F., Wagner, D., Weihe, K.: Dijkstra’s algorithm on-line: An empirical case study from public railroad transport. Journal of Experimental Algorithmics, 5(12) (2000)

    Google Scholar 

  34. Schulz, F., Wagner, D., Zaroliagis, C.: Using multi-level graphs for timetable information in railway systems. In: Mount, D.M., Stein, C. (eds.) ALENEX 2002. LNCS, vol. 2409, pp. 43–59. Springer, Heidelberg (2002)

    Google Scholar 

  35. Theune, D.: Robuste und effiziente Methoden zur Lösung von Wegproblemen. Teubner Verlag, Stuttgart (1995)

    Google Scholar 

  36. Tsaggouris, G., Zaroliagis, C.: Multiobjective optimization: Improved FPTAS for shortest paths and non-linear objectives with applications. Theory of Computing Systems (to appear, 2007)

    Google Scholar 

  37. Tulp, E., Siklóssy, L.: TRAINS, an active time-table searcher. In: Eighth European Conf. on AI, pp. 170–175 (1988)

    Google Scholar 

  38. Vassilvitskii, S., Yannakakis, M.: Efficiently computing succinct trade-off curves. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1201–1213. Springer, Heidelberg (2004)

    Google Scholar 

  39. Wagner, D., Willhalm, T.: Speed-up techniques for shortest-path computations. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 23–36. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  40. Wagner, D., Willhalm, T., Zaroliagis, C.: Geometric containers for efficient shortest-path computation. ACM Journal of Experimental Algorithmics, 10 (2005)

    Google Scholar 

  41. Warburton, A.: Approximation of pareto optima in multiple-objective shortest path problems. Operations Research 35, 70–79 (1987)

    MATH  MathSciNet  Google Scholar 

  42. White, D.J.: Epsilon efficiency. Jorunal of Optimization Theory and Applications 49, 319–337 (1986)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Darmstadt University of Technology, Department of Computer Science, Algorithmics Group, Hochschulstr. 10, 64289 Darmstadt, Germany

    Matthias Müller-Hannemann

  2. University of Karlsruhe, Department of Computer Science, P.O. Box 6980, 76128 Karlsruhe, Germany

    Frank Schulz & Dorothea Wagner

  3. Computer Technology Institute, P.O. Box 1122, 26110 Patras, Greece, and Department of Computer Engineering and Informatics, University of Patras, 26500 Patras, Greece

    Christos Zaroliagis

Authors
  1. Matthias Müller-Hannemann
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  2. Frank Schulz
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  3. Dorothea Wagner
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  4. Christos Zaroliagis
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Editor information

Frank Geraets Leo Kroon Anita Schoebel Dorothea Wagner Christos D. Zaroliagis

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Müller-Hannemann, M., Schulz, F., Wagner, D., Zaroliagis, C. (2007). Timetable Information: Models and Algorithms. In: Geraets, F., Kroon, L., Schoebel, A., Wagner, D., Zaroliagis, C.D. (eds) Algorithmic Methods for Railway Optimization. Lecture Notes in Computer Science, vol 4359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74247-0_3

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  • DOI: https://doi.org/10.1007/978-3-540-74247-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74245-6

  • Online ISBN: 978-3-540-74247-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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