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A Note on the Complexity of Dijkstra's Algorithm for Graphs with Weighted Vertices
February 1998 (vol. 47 no. 2)
pp. 263

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 ${\cal O}(|E| + |V|\ \log\ |V|).$

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Index Terms:
Analysis of algorithms, combinatorial problems, data structures
Michael Barbehenn, "A Note on the Complexity of Dijkstra's Algorithm for Graphs with Weighted Vertices," IEEE Transactions on Computers, vol. 47, no. 2, pp. 263, Feb. 1998, doi:10.1109/12.663776
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