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All-Pairs Shortest Paths with Real Weights in O(n 3/log n) Time

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Abstract

We describe an O(n 3/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (SIAM J. Comput. 5:49–60, 1976), Takaoka (Inform. Process. Lett. 43:195–199, 1992), Dobosiewicz (Int. J. Comput. Math. 32:49–60, 1990), Han (Inform. Process. Lett. 91:245–250, 2004), Takaoka (Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, pp. 278–289, Springer, 2004), and Zwick (Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, pp. 921–932, Springer, 2004). The new algorithm is surprisingly simple and different from previous ones.

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Authors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Timothy M. Chan

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  1. Timothy M. Chan
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Correspondence to Timothy M. Chan.

Additional information

A preliminary version of this paper appeared in Proc. 9th Workshop Algorithms Data Struct. (WADS), Lect. Notes Comput. Sci., vol. 3608, pp. 318–324, Springer, 2005.

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Chan, T.M. All-Pairs Shortest Paths with Real Weights in O(n 3/log n) Time. Algorithmica 50, 236–243 (2008). https://doi.org/10.1007/s00453-007-9062-1

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