A Note on the Complexity of Dijkstra's Algorithm for Graphs with Weighted Vertices

Authors:
Michael Barbehenn
Affiliations:
Motorola GmbH, Germany
Venue:
IEEE Transactions on Computers
Year:
1998

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Abstract

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