Journal of Combinatorial Optimization

, Volume 25, Issue 2, pp 326–337 | Cite as

A simplified algorithm for the all pairs shortest path problem with O(n 2logn) expected time

  • Tadao Takaoka


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 so far 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 nn/logn. In this paper, we remove the concept of critical point, whereby we make the algorithm simpler and seamless, resulting in a simpler analysis.


Algorithm All pairs shortest paths Expected time Priority queue 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of CanterburyChristchurchNew Zealand

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