Abstract
The best known expected time for the all pairs shortest path problem on a directed graph with non-negative edge costs is O(n 2logn) by Moffat and Takaoka. Let the solution set be the set of vertices to which the given algorithm has established shortest paths. The Moffat-Takaoka algorithm maintains complexities before and after the critical point in balance, which is the moment when the size of the solution set is nāāān/logn. In this paper, we remove the concept of critical point and the data structure, called a batch list, whereby we make the algorithm simpler and seamless, resulting in a simpler analysis and speed-up.
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
Blelloch, G.E., Vassilevska, V., Williams, R.: A New Combinatorial Approach for Sparse Graph Problems. In: Aceto, L., DamgĆ„rd, I., Goldberg, L.A., HalldĆ³rsson, M.M., IngĆ³lfsdĆ³ttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol.Ā 5125, pp. 108ā120. Springer, Heidelberg (2008)
Bloniarz, P.: A shortest path algorithm with expected time O(n 2lognlog* n). SIAM Journal on ComputingĀ 12, 588ā600 (1983)
Chan, T.: More algorithms for all pairs shortest paths. In: STOC 2007, pp. 590ā598 (2007)
Dantzig, G.: On the shortest route in a network. Management ScienceĀ 6, 269ā271 (1960)
Feller, W.H.: An Introduction to Probability and its Applications, 3rd edn., vol.Ā 1. John-Wiley, New York (1968)
Fredman, M., Tarjan, R.: Fibonacci heaps and their uses in improved network optimization problems. JACMĀ 34, 596ā615 (1987)
Goldberg, A.V., Tarjan, R.E.: Expected Performance of Dijkstraās Shortest Path Algorithm, Technical Report 96-062, NEC Research Institute, Inc. (June 1996)
Mehlhorn, K., Priebe, V.: On the All-Pairs Shortest Path Algorithm of Moffat and Takaoka. Random Structures and AlgorithmsĀ 10, 205ā220 (1997)
Moffat, A., Takaoka, T.: An all pairs shortest path algorithm with expected running time O(n 2logn). SIAM Journal on ComputingĀ 16, 1023ā1031 (1987)
Pettie, S.: A new approach to all pairs shortest paths on real weighted graphs. Theoretical Computer ScienceĀ 312, 47ā74 (2004)
Spira, P.: A new algorithm for finding all shortest paths in a graph of positive arcs in average time O(n 2log2 n). SIAM Journal on ComputingĀ 2, 28ā32 (1973)
Takaoka, T., Moffat, A.: An O(n 2lognloglogn) expected time algorithm for the all pairs shortest path problem. In: Dembinski, P. (ed.) MFCS 1980. LNCS, vol.Ā 88, pp. 643ā655. Springer, Heidelberg (1980)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
Ā© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Takaoka, T., Hashim, M. (2010). A Simpler Algorithm for the All Pairs Shortest Path Problem with O(n 2logn) Expected Time. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17461-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-17461-2_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17460-5
Online ISBN: 978-3-642-17461-2
eBook Packages: Computer ScienceComputer Science (R0)