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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
Citation:
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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