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

Shortest Paths
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Shortest Paths
Figure: The shortest path from to t can pass through many intermediate vertices.
The shortest path between two vertices and t in an unweighted graph can be constructed using a breadthfirst
search from . When we first encounter t in the search, we will have reached it from using the
minimum number of possible edges. This minimum-link path is recorded in the breadth-first search tree,
and it provides the shortest path when all edges have equal weight. However, in an arbitrary weighted
graph, the weight of a path between two vertices is the sum of the weights of the edges along the path.
The shortest path might use a large number of edges, just as the shortest route (timewise) from home to
office may involve shortcuts using backroads and many turns, as shown in Figure .
Shortest paths have a surprising variety of applications. See catalog Section and the war story of
Section for further examples.
● Dijkstra's Algorithm
● All-Pairs Shortest Path
Algorithms
Mon Jun 2 23:33:50 EDT 1997
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