Abstract
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.
This work was supported by Texas Advanced Research Program Grant 003658-0029-1999 and NSF Grant CCR-9988160. Seth Pettie was also supported by an MCD Graduate Fellowship.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. V. Aho, J. E. Hopcroft, J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.
B. Bollobás. Random Graphs. Academic Press, London, 1985.
B. V. Cherkassky, A. V. Goldberg, T. Radzik. Shortest paths algorithms: Theory and experimental evaluation. In Math. Prog. 73 (1996), 129–174.
T. Cormen, C. Leiserson, R. Rivest. Intro. to Algorithms. MIT Press, 1990.
E. W. Dijkstra. A note on two problems in connexion with graphs. In Numer. Math., 1 (1959), 269–271.
P. Erdös, A. Rényi On the evolution of random graphs. Bull. Inst. Internat. Statist. 38, pp. 343–347, 1961.
M. Fredman. New bounds on the complexity of the shortest path problem. SIAM J. Comput. 5 (1976), no. 1, 83–89.
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.
M. L. Fredman, R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. In JACM 34 (1987), 596–615.
H. N. Gabow. A scaling algorithm for weighted matching on general graphs. In Proc. FOCS 1985, 90–99.
A. Goldberg. A simple shortest path algorithm with linear average time. InterTrust Technical Report STAR-TR-01-03, March 2001.
A. Goldberg. Shortest path algorithms: engineering aspects. ISSAC 2001.
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.
T. Hagerup. Improved shortest paths on the word RAM. In Proc. ICALP 2000, LNCS volume 1853, 61–72.
J. Iacono. Improved upper bounds for pairing heaps. Algorithm theory—SWAT 2000 (Bergen), LNCS vol. 1851, 32–45
H. Jakobsson, Mixed-approach algorithms for transitive closure. In Proc. ACM PODS, 1991, pp. 199–205.
V. Jarník, O jistém problému minimálním. Práca Moravské Prírodovedecké Spolecnosti 6 (1930), 57–63, in Czech.
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.
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.
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.
K. Mehlhorn, S. Näher. The LEDA Platform of Combinatorial and Geometric Computing. Cambridge Univ. Press, 1999.
U. Meyer. Single source shortest paths on arbitrary directed graphs in linear average-case time. In Proc. SODA 2001, 797–806.
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.
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.
S. Pettie, V. Ramachandran. An optimal minimum spanning tree algorithm. In Proc. ICALP 2000, LNCS volume 1853, 49–60. JACM, to appear.
S. Pettie, V. Ramachandran. Computing shortest paths with comparisons and additions. In Proc. SODA’ 02, January 2002, to appear.
P. Sanders. Fast priority queues for cached memory. J. Experimental Algorithms 5, article 7, 2000.
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.
M. Thorup. Undirected single source shortest paths with positive integer weights in linear time. J. Assoc. Comput. Mach. 46 (1999), no. 3, 362–394.
M. Thorup. Quick k-median, k-center, and facility location for sparse graphs. In Proc. ICALP 2001, LNCS Vol. 2076, 249–260.
U. Zwick. Exact and approximate distances in graphs — a survey. In Proc. 9th ESA (2001), 33–48. Updated copy at http://www.cs.tau.ac.il/~zwick
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pettie, S., Ramachandran, V., Sridhar, S. (2002). Experimental Evaluation of a New Shortest Path Algorithm. In: Mount, D.M., Stein, C. (eds) Algorithm Engineering and Experiments. ALENEX 2002. Lecture Notes in Computer Science, vol 2409. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45643-0_10
Download citation
DOI: https://doi.org/10.1007/3-540-45643-0_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43977-6
Online ISBN: 978-3-540-45643-8
eBook Packages: Springer Book Archive