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A note on the complexity of Dijkstra's algorithm for graphs with weighted vertices

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1 Author(s)
Barbehenn, M. ; Motorola GmbH, Munchen, Germany

Let G(V, E) be a directed graph in which each vertex has a nonnegative weight. The cost of a path between two vertices in G is the sum of the weights of the vertices on that path. We show that, for such graphs, the time complexity of Dijkstra's algorithm (E.W. Dijkstra, 1959), implemented with a binary heap, is O(|E|+|V|log|V|)

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Computers, IEEE Transactions on  (Volume:47 ,  Issue: 2 )