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Travel Planning with Self-Made Maps

  • Ulrik Brandes
  • Frank Schulz
  • Dorothea Wagner
  • Thomas Willhalm
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2153)

Abstract

Speed-up techniques that exploit given node coordinates have proven useful for shortest-path computations in transportation networks and geographic information systems. To facilitate the use of such techniques when coordinates are missing from some, or even all, of the nodes in a network we generate artificial coordinates using methods from graph drawing. Experiments on a large set of German train timetables indicate that the speed-up achieved with coordinates from our network drawings is close to that achieved with the actual coordinates.

Keywords

Short Path Graph Drawing Layout Algorithm Query Response Time Travel Planning 
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.K. Ahuja, T.L. Magnanti, and J.B. Orlin. Network Flows. Prentice-Hall, 1993.Google Scholar
  2. 2.
    J. Branke, F. Bucher, and H. Schmeck. A genetic algorithm for drawing undirected graphs. Proc. 3rd Nordic Workshop on Genetic Algorithms and their Applications, pp. 193–206, 1997.Google Scholar
  3. 3.
    R. L. Brooks, C. A. B. Smith, A. H. Stone, and W. T. Tutte. The dissection of rectangles into squares. Duke Mathematical Journal, 7:312–340, 1940.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    I. F. Cruz and J. P. Twarog. 3D graph drawing with simulated annealing. Proc. 3rd Intl. Symp. Graph Drawing (GD’ 95), Springer LNCS 1027, pp. 162–165, 1996.CrossRefGoogle Scholar
  5. 5.
    R. Davidson and D. Harel. Drawing graphs nicely using simulated annealing. ACM Transactions on Graphics, 15(4):301–331, 1996.CrossRefGoogle Scholar
  6. 6.
    P. Eades. A heuristic for graph drawing. Congressus Numerantium, 42:149–160, 1984.MathSciNetGoogle Scholar
  7. 7.
    P. Eades and N. C. Wormald. Fixed edge-length graph drawing is np-hard. Discrete Applied Mathematics, 28:111–134, 1990.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    T. M. Fruchterman and E. M. Reingold. Graph-drawing by force-directed placement. Software—Practice and Experience, 21(11):1129–1164, 1991.CrossRefGoogle Scholar
  9. 9.
    P. Gajer, M. T. Goodrich, and S. G. Kobourov. A fast multi-dimensional algorithm for drawing large graphs. Proc. Graph Drawing 2000. To appear.Google Scholar
  10. 10.
    G. H. Golub and C. F. van Loan. Matrix Computations. Johns Hopkins University Press, 3rd edition, 1996.Google Scholar
  11. 11.
    D. Harel and Y. Koren. A fast multi-scale method for drawing large graphs. Proc. Graph Drawing 2000. To appear.Google Scholar
  12. 12.
    S. Jung and S. Pramanik. HiTi graph model of topographical road maps in navigation systems. Proc. 12th IEEE Int. Conf. Data Eng., pp. 76–84, 1996.Google Scholar
  13. 13.
    T. Kamada and S. Kawai. An algorithm for drawing general undirected graphs. Information Processing Letters, 31:7–15, 1989.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    C. Kosak, J. Marks, and S. Shieber. Automating the layout of network diagrams with specified visual organization. IEEE Transactions on Systems, Man and Cybernetics, 24(3):440–454, 1994.CrossRefGoogle Scholar
  15. 15.
    P. Kosmol. Methoden zur numerischen Behandlung nichtlinearer Gleichungen und Optimierungsaufgaben. Teubner Verlag, 1993.Google Scholar
  16. 16.
    T. Lengauer. Combinatorial Algorithms for Integrated Circuit Layout. Wiley, 1990.Google Scholar
  17. 17.
    K. Nachtigall. Time depending shortest-path problems with applications to railway networks. European Journal of Operational Research 83:154–166, 1995.zbMATHCrossRefGoogle Scholar
  18. 18.
    T. Preuß and J.-H. Syrbe. An integrated traffic information system. Proc. 6th Intl. EuropIA Conf. Appl. Computer Networking in Architecture, Construction, Design, Civil Eng., and Urban Planning. Europia Productions, 1997.Google Scholar
  19. 19.
    F. Schulz, D. Wagner, and K. Weihe. Dijkstra’s algorithm on-line: an empirical case study from public railroad transport. Proc. 3rd Workshop on Algorithm Engineering (WAE’ 99), Springer LNCS 1668, pp. 110–123, 1998.Google Scholar
  20. 20.
    R. Sedgewick and J. S. Vitter. Shortest paths in euclidean space. Algorithmica 1:31–48, 1986.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    S. Shekhar, A. Kohli, and M. Coyle. Path computation algorithms for advanced traveler information system (ATIS). Proc. 9th IEEE Intl. Conf. Data Eng., pp. 31–39, 1993.Google Scholar
  22. 22.
    L. Siklóssy and E. Tulp. TRAINS, an active time-table searcher. Proc. 8th European Conf. Artificial Intelligence, pp. 170–175, 1988.Google Scholar
  23. 23.
    P. Spellucci. Numerische Verfahren der nichtlinearen Optimierung. Birkhäuser Verlag, 1993.Google Scholar
  24. 24.
    D. Tunkelang. JIGGLE: Java interactive general graph layout environment. Proc. 6th Intl. Symp. Graph Drawing (GD’ 98), Springer LNCS 1547, pp. 413–422, 1998.Google Scholar
  25. 25.
    W. T. Tutte. How to draw a graph. Proceedings of the London Mathematical Society, Third Series, 13:743–768, 1963.zbMATHMathSciNetCrossRefGoogle Scholar
  26. 26.
    C. Walshaw. A multilevel algorithm for force-directed graph drawing. Proc. Graph Drawing 2000. To appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Frank Schulz
    • 1
  • Dorothea Wagner
    • 1
  • Thomas Willhalm
    • 1
  1. 1.Department of Computer & Information ScienceUniversity of KonstanzKonstanzGermany

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