Experimental Evaluation of a New Shortest Path Algorithm

Extended Abstract
  • Seth Pettie
  • Vijaya Ramachandran
  • Srinath Sridhar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2409)


We evaluate the practical efficiency of a new shortest path algorithm for undirected graphs which was developed by the first two authors. This algorithm works on the fundamental comparison-addition model.

Theoretically, this new algorithm out-performs Dijkstra’s algorithm on sparse graphs for the all-pairs shortest path problem, and more generally, for the problem of computing single-source shortest paths from ω(1) different sources. Our extensive experimental analysis demonstrates that this is also the case in practice. We present results which show the new algorithm to run faster than Dijkstra’s on a variety of sparse graphs when the number of vertices ranges from a few thousand to a few million, and when computing single-source shortest paths from as few as three different sources.


Short Path Minimum Span Tree Short Path Problem Graph Class 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AHU74]
    A. V. Aho, J. E. Hopcroft, J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.Google Scholar
  2. [Bo85]
    B. Bollobás. Random Graphs. Academic Press, London, 1985.zbMATHGoogle Scholar
  3. [CGR96]
    B. V. Cherkassky, A. V. Goldberg, T. Radzik. Shortest paths algorithms: Theory and experimental evaluation. In Math. Prog. 73 (1996), 129–174.MathSciNetGoogle Scholar
  4. [CLR90]
    T. Cormen, C. Leiserson, R. Rivest. Intro. to Algorithms. MIT Press, 1990.Google Scholar
  5. [Dij59]
    E. W. Dijkstra. A note on two problems in connexion with graphs. In Numer. Math., 1 (1959), 269–271.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [ER61]
    P. Erdös, A. Rényi On the evolution of random graphs. Bull. Inst. Internat. Statist. 38, pp. 343–347, 1961.zbMATHMathSciNetGoogle Scholar
  7. [F76]
    M. Fredman. New bounds on the complexity of the shortest path problem. SIAM J. Comput. 5 (1976), no. 1, 83–89.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [F+86]
    M. L. Fredman, R. Sedgewick, D. D. Sleator, R. E. Tarjan. The pairing heap: A new form of self-adjusting heap. In Algorithmica 1 (1986) pp. 111–129.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [FT87]
    M. L. Fredman, R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. In JACM 34 (1987), 596–615.CrossRefMathSciNetGoogle Scholar
  10. [G85]
    H. N. Gabow. A scaling algorithm for weighted matching on general graphs. In Proc. FOCS 1985, 90–99.Google Scholar
  11. [G01]
    A. Goldberg. A simple shortest path algorithm with linear average time. InterTrust Technical Report STAR-TR-01-03, March 2001.Google Scholar
  12. [G01b]
    A. Goldberg. Shortest path algorithms: engineering aspects. ISSAC 2001.Google Scholar
  13. [GS97]
    A. Goldberg, C. Silverstein. Implementations of Dijkstra’s algorithm based on multi-level buckets. Network optimization (1997), Lec. Not. Econ. Math. Syst. 450, 292–327.Google Scholar
  14. [Hag00]
    T. Hagerup. Improved shortest paths on the word RAM. In Proc. ICALP 2000, LNCS volume 1853, 61–72.Google Scholar
  15. [Iac00]
    J. Iacono. Improved upper bounds for pairing heaps. Algorithm theory—SWAT 2000 (Bergen), LNCS vol. 1851, 32–45CrossRefGoogle Scholar
  16. [Jak91]
    H. Jakobsson, Mixed-approach algorithms for transitive closure. In Proc. ACM PODS, 1991, pp. 199–205.Google Scholar
  17. [Jar30]
    V. Jarník, O jistém problému minimálním. Práca Moravské Prírodovedecké Spolecnosti 6 (1930), 57–63, in Czech.Google Scholar
  18. [KKP93]
    D. R. Karger, D. Koller, S. J. Phillips. Finding the hidden path: time bounds for all-pairs shortest paths. SIAM J. on Comput. 22 (1993), no. 6, 1199–1217.zbMATHCrossRefMathSciNetGoogle Scholar
  19. [KS98]
    S. Kolliopoulos, C. Stein. Finding real-valued single-source shortest paths in o(n 3) expected time. J. Algorithms 28 (1998), no. 1, 125–141.zbMATHCrossRefMathSciNetGoogle Scholar
  20. [McG91]
    C. C. McGeoch. A new all-pairs shortest-path algorithm. Tech. Report 91-30 DIMACS, 1991. Also appears in Algorithmica, 13(5): 426–461, 1995.Google Scholar
  21. [MN99]
    K. Mehlhorn, S. Näher. The LEDA Platform of Combinatorial and Geometric Computing. Cambridge Univ. Press, 1999.Google Scholar
  22. [Mey01]
    U. Meyer. Single source shortest paths on arbitrary directed graphs in linear average-case time. In Proc. SODA 2001, 797–806.Google Scholar
  23. [MT87]
    A. Moffat, T. Takaoka. An all pairs shortest path algorithm with expected time O(n 2log n). SIAM J. Comput. 16 (1987), no. 6, 1023–1031.zbMATHCrossRefMathSciNetGoogle Scholar
  24. [MS94]
    B. M. E. Moret, H. D. Shapiro. An empirical assessment of algorithms for constructing a minimum spanning tree. In DIMACS Series on Discrete Math. and Theor. CS, 1994.Google Scholar
  25. [PR00]
    S. Pettie, V. Ramachandran. An optimal minimum spanning tree algorithm. In Proc. ICALP 2000, LNCS volume 1853, 49–60. JACM, to appear.Google Scholar
  26. [PR02]
    S. Pettie, V. Ramachandran. Computing shortest paths with comparisons and additions. In Proc. SODA’ 02, January 2002, to appear.Google Scholar
  27. [S00]
    P. Sanders. Fast priority queues for cached memory. J. Experimental Algorithms 5, article 7, 2000.Google Scholar
  28. [Tak92]
    T. Takaoka. A new upper bound on the complexity of the all pairs shortest path problem. Inform. Process. Lett. 43 (1992), no. 4, 195–199.zbMATHCrossRefMathSciNetGoogle Scholar
  29. [Tho99]
    M. Thorup. Undirected single source shortest paths with positive integer weights in linear time. J. Assoc. Comput. Mach. 46 (1999), no. 3, 362–394.zbMATHMathSciNetGoogle Scholar
  30. [Tho01]
    M. Thorup. Quick k-median, k-center, and facility location for sparse graphs. In Proc. ICALP 2001, LNCS Vol. 2076, 249–260.Google Scholar
  31. [Z01]
    U. Zwick. Exact and approximate distances in graphs — a survey. In Proc. 9th ESA (2001), 33–48. Updated copy at

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Seth Pettie
    • 1
  • Vijaya Ramachandran
    • 1
  • Srinath Sridhar
    • 1
  1. 1.Department of Computer SciencesThe University of Texas at AustinAustin

Personalised recommendations