Johnson's algorithm: Difference between revisions

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Revision as of 21:53, 19 October 2016

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==Analysis==

The [[time complexity]] of this algorithm, using [[Fibonacci heap]]s in the implementation of Dijkstra's algorithm, is {{<math|>O(''|V''^{|^2}\log ''|V''| + ''VE''|V||E|)}})</math>: the algorithm uses {{<math|>O(''VE''|V||E|)}}</math> time for the Bellman–Ford stage of the algorithm, and {{<math|>O(''|V'' |\log ''|V''| + ''|E''|)}}</math> for each of {{the <math>|''V''}}|</math> instantiations of Dijkstra's algorithm. Thus, when the graph is sparse, the total time can be faster than the [[Floyd–Warshall algorithm]], which solves the same problem in time {{<math|>O(''|V''<sup>|^3)</supmath>)}}.<ref name="clrs"/>

==References==