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

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

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...

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Veröffentlicht in:IEEE transactions on computers 1998-02, Vol.47 (2), p.263-263
1. Verfasser: Barbehenn, M.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science
control theory
systems
Cost function
Data structures
Exact sciences and technology
Orbital robotics
Space exploration
Testing
Theoretical computing
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Zusammenfassung: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|).
ISSN:0018-9340
1557-9956
DOI:10.1109/12.663776