July 2018
Beginner
202 pages
5h 4m
English
Content preview from Beginning Java Data Structures and Algorithms
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All Pairs Shortest Paths: Floyd-Warshall Algorithm
Sometimes, it might be necessary to compute the shortest paths between all pairs of vertices. For example, we might be interested in building a table of distances. One way to do that is to perform a single source shortest path for every vertex of the graph. If you use Dijkstra's algorithm for that, we end up with a runtime of O(V*(V + E)logE).
In this subsection, we shall explore an algorithm capable of solving the all pairs shortest paths problem in O(V3) time, with a remarkably simple and elegant implementation.
The algorithm we are about to study, more commonly referred to as the Floyd-Warshall algorithm, was published in its current form by Robert Floyd in 1962. However, in its essence, ...
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