Acceleration of Shortest Path and Constrained Shortest Path Computation

  • Ekkehard Köhler
  • Rolf H. Möhring
  • Heiko Schilling
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)


We study acceleration methods for point-to-point shortest path and constrained shortest path computations in directed graphs, in particular in road and railroad networks. Our acceleration methods are allowed to use a preprocessing of the network data to create auxiliary information which is then used to speed-up shortest path queries. We focus on two methods based on Dijkstra’s algorithm for shortest path computations and two methods based on a generalized version of Dijkstra for constrained shortest paths. The methods are compared with other acceleration techniques, most of them published only recently. We also look at appropriate combinations of different methods to find further improvements. For shortest path computations we investigate hierarchical multiway-separator and arc-flag approaches. The hierarchical multiway-separator approach divides the graph into regions along a multiway-separator and gathers information to improve the search for shortest paths that stretch over several regions. A new multiway-separator heuristic is presented which improves the hierarchical separator approach. The arc-flag approach divides the graph into regions and gathers information on whether an arc is on a shortest path into a given region. Both methods yield significant speed-ups of the plain Dijkstra’s algorithm. The arc flag method combined with an appropriate partition and a bi-directed search achieves an average speed-up of up to 1,400 on large networks. This combination narrows down the search space of Dijkstra’s algorithm to almost the size of the corresponding shortest path for long distance shortest path queries. For the constrained shortest path problem we show that goal-directed and bi-directed acceleration methods can be used both individually and in combination. The goal-directed search achieves the best speed-up factor of 110 for the constrained problem.


Short Path Target Node Short Path Problem Railroad Network Acceleration Method 
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  1. 1.
    Aneja, Y.P., Aggarwal, V., Nair, K.P.K.: Shortest chain subject to side constraints. Networks 13, 295–302 (1983)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Czarnecki, K., Eisenecker, U.W.: Generative programming: methods, tools, and applications. ACM Press/Addison-Wesley Publishing Co (2000)Google Scholar
  3. 3.
    Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Mathematik, 269–271 (1955)Google Scholar
  4. 4.
    Dumitrescu, I.: Constrained path and cycle problems. PhD thesis, The University of Melbourne (2002)Google Scholar
  5. 5.
    Frederickson, G.N.: Fast algorithms for shortest paths in planar graphs, with applications. SIAM J. Comput. 16, 1004–1022 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Goldberg, A.V., Harrelson, C.: Computing the shortest path: A * search meets graph theory. In: Proc. of the 16th Annual ACM-SIAM Symp. on Discrete Algorithms, pp. 156–165 (2005)Google Scholar
  7. 7.
    Goodrich, M.T.: Planar Separators and Parallel Polygon Triangulation. Journal of Computer and System Sciences 51, 374–389 (1995)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Gutman, R.: Reach-based routing: A new approach to shortest path algorithms optimized for road networks. In: Proc. of the 6th ALENEX 2004, pp. 100–111 (2004)Google Scholar
  9. 9.
    Holzer, M., Schulz, F., Willhalm, T.: Combining speed-up techniques for shortest-path computations. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 269–284. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Jahn, O., Möhring, R.H., Schulz, A.S., Moses, N.E.S.: System optimal routing of traffic flows with user constraints in networks with congestion. Oper. Res (2005) (to appear)Google Scholar
  11. 11.
    Köhler, E., Möhring, R.H., Schilling, H.: Acceleration of shortest path and constrained shortest path computation. Technical Report Report-042-2004, TU Berlin (2004)Google Scholar
  12. 12.
    Lauther, U.: Slow preprocessing of graphs for extremely fast shortest path calculations. In: Lecture at the Workshop on Computational Integer Programming at ZIB (1997)Google Scholar
  13. 13.
    Lauther, U.: An extremely fast, exact algorithm for finding shortest paths in static networks with geographical background. In: Raubal, M., Sliwinski, A., Kuhn, W. (eds.) Geoinformation und Mobilität. IfGI prints, vol. 22, pp. 22–32. Institut für Geoinformatik, Münster (2004)Google Scholar
  14. 14.
    Mehlhorn, K., Ziegelmann, M.: Resource constrained shortest paths. In: Paterson, M. (ed.) ESA 2000. LNCS, vol. 1879, pp. 326–337. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Metis: A family of multilevel partitioning algorithms (2003),
  16. 16.
    Möhring, R.H., Schilling, H., Schütz, B., Wagner, D., Willhalm, T.: Partitioning graphs to speed up Dijkstra’s algorithm. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 189–202. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Müller-Hannemann, M., Schnee, M.: Finding all attractive train connections by multi-criteria pareto search. In: 4th Workshop on Algorithmic Methods and Models for Optimization of Railways (2004) (to appear)Google Scholar
  18. 18.
    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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Ekkehard Köhler
    • 1
  • Rolf H. Möhring
    • 1
  • Heiko Schilling
    • 1
  1. 1.Institut für MathematikTU BerlinBerlinGermany

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