, Volume 50, Issue 2, pp 236–243 | Cite as

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

  • Timothy M. ChanEmail author


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.


Shortest paths Graph algorithms 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.School of Computer ScienceUniversity of WaterlooWaterlooCanada

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