The.Algorithm.Design.Manual.Springer-Verlag.1998

Dijkstra's Algorithm
To be certain of finding the shortest path between and t, we might have to first find the shortest path between and all other
vertices. This defines a shortest path spanning tree rooted in . For undirected graphs, this will be the breadth-first search tree,
but in general it provides the shortest path between and all other vertices.
What is the running time of this algorithm? When implemented using adjacency lists and a Boolean array to mark what is
known about each vertex, the complexity is . This is the same running time as a proper version of Prim's algorithm;
indeed, except for the extension condition, it is the same algorithm as Prim's.
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Algorithms
Mon Jun 2 23:33:50 EDT 1997
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