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Using Multi-level Graphs for Timetable Information in Railway Systems

  • Frank Schulz
  • Dorothea Wagner
  • Christos Zaroliagis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2409)

Abstract

In many fields of application, shortest path finding problems in very large graphs arise. Scenarios where large numbers of on-line queries for shortest paths have to be processed in real-time appear for example in traffic information systems. In such systems, the techniques considered to speed up the shortest path computation are usually based on precomputed information. One approach proposed often in this context is a space reduction, where precomputed shortest paths are replaced by single edges with weight equal to the length of the corresponding shortest path. In this paper, we give a first systematic experimental study of such a space reduction approach. We introduce the concept of multi-level graph decomposition. For one specific application scenario from the field of timetable information in public transport, we perform a detailed analysis and experimental evaluation of shortest path computations based on multi-level graph decomposition.

Keywords

Short Path Station Graph Original Graph Short Path Problem Short Path Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. Agrawal and H. Jagadish. Algorithms for Searching Massive Graphs. IEEE Transact. Knowledge and Data Eng., Vol. 6, 225–238, 1994.CrossRefGoogle Scholar
  2. 2.
    C. Barrett, R. Jacob, and M. Marathe. Formal-Language-Constrained Path Problems. SIAM Journal on Computing, Vol. 30, No. 3, 809–837, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    U. Brandes, F. Schulz, D. Wagner, and T. Willhalm. Travel Planning with Self-Made Maps. Proc. 3rd Workshop Algorithm Engineering and Experiments (ALENEX’ 01), Springer LNCS Vol. 2153, 132–144, 2001.Google Scholar
  4. 4.
    A. Car and A. Frank. Modelling a Hierarchy of Space Applied to Large Road Networks. Proc. Int. Worksh. Adv. Research Geogr. Inform. Syst. (IGIS’ 94), 15–24, 1994.Google Scholar
  5. 5.
    S. Chaudhuri and C. Zaroliagis. Shortest Paths in Digraphs of Small Treewidth. Part II: Optimal Parallel Algorithms. Theoretical Computer Science, Vol. 203, No. 2, 205–223, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    S. Chaudhuri and C. Zaroliagis. Shortest Paths in Digraphs of Small Treewidth. Part I: Sequential Algorithms. Algorithmica, Vol. 27, No. 3, 212–226, Special Issue on Treewidth, 2000.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    G. Frederickson. Planar graph decomposition and all pairs shortest paths. Journal of the ACM, Vol. 38, Issue 1, 162–204, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    G. Frederickson. Using Cellular Graph: Embeddings in Solving All Pairs Shortest Path Problems. Journal of Algorithms, Vol. 19, 45–85, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    http://bahn.hafas.de. Hafas is a trademark of Hacon Ingenieurgesellschaft mbH, Hannover, Germany.
  10. 10.
    M. Müller-Hannemann and K. Weihe. Pareto Shortest Paths is Often Feasible in Practice. Proc. 5th Workshop on Algorithm Engineering (WAE’01), Springer LNCS 2141, 185–197, 2001.Google Scholar
  11. 11.
    K. Ishikawa, M. Ogawa, S. Azume, and T. Ito. Map Navigation Software of the Electro Multivision of the’ 91 Toyota Soarer. IEEE Int. Conf. Vehicle Navig. Inform. Syst., 463–473, 1991.Google Scholar
  12. 12.
    R. Jakob, M. Marathe, and K. Nagel. A Computational Study of Routing Algorithms for Realistic Transportation Networks. The ACM Journal of Experimental Algorithmics, Vol. 4, Article 6, 1999.Google Scholar
  13. 13.
    S. Jung and S. Pramanik. HiTi Graph Model of Topographical Road Maps in Navigation Systems. Proc. 12th IEEE Int. Conf. Data Eng., 76–84, 1996.Google Scholar
  14. 14.
    D. Kavvadias, G. Pantziou, P. Spirakis, and C. Zaroliagis. Hammock-on-Ears Decomposition: A Technique for the Efficient Parallel Solution of Shortest Paths and Other Problems. Theoretical Computer Science, Vol. 168, No. 1, 121–154, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    T. Preuss and J.-H. Syrbe. An Integrated Traffic Information System. Proc. 6th Int. Conf. Appl. Computer Networking in Architecture, Construction, Design, Civil Eng., and Urban Planning (europIA’ 97), 1997.Google Scholar
  16. 16.
    S. Shekhar, A. Fetterer, and G. Goyal. Materialization trade-offs in hierarchical shortest path algorithms. Proc. Int. Symp. Large Spatial Databases, Springer LNCS 1262, 94–111, 1997.Google Scholar
  17. 17.
    S. Shekhar, A. Kohli, and M. Coyle. Path Computation Algorithms for Advanced Traveler Information System (ATIS). Proc. 9th IEEE Int. Conf. Data Eng., 31–39, 1993.Google Scholar
  18. 18.
    J. Shapiro, J. Waxman, and D. Nir. Level Graphs and Approximate Shortest Path Algorithms. Network 22, 691–717, 1992.zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    L. Siklóssy and E. Tulp. The Space Reduction Method: A method to reduce the size of search spaces. Information Processing Letters, 38(4), 187–192, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    F. Schulz, D. Wagner, and K. Weihe. Dijkstra’s Algorithm On-Line: An Empirical Study from Public Railroad Study. ACM Journal of Experimental Algorithmics, Vol. 5, Article 12, 2000, Special issue on WAE’99.Google Scholar
  21. 21.
    J. D. Ullman and M. Yannakakis, High Probability Parallel Transitive Closure Algorithms, SIAM J. on Computing 20(1), pp. 100–125, 1991.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Frank Schulz
    • 1
    • 2
  • Dorothea Wagner
    • 1
  • Christos Zaroliagis
    • 2
  1. 1.Department of Computer and Information ScienceUniversity of KonstanzKonstanzGermany
  2. 2.Computer Technology Institute, and Department of Computer Engineering & InformaticsUniversity of PatrasPatrasGreece

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