The Floyd-Warshall algorithm, also variously known as Floyd's algorithm, the Roy-Floyd algorithm, the Roy-Warshall algorithm, or the WFI algorithm, is an algorithm for efficiently and simultaneously finding the shortest paths (i.e., graph geodesics) between every pair of vertices in a weighted and potentially directed graph. The Floyd algorithm is essentially equivalent to the transitive closure algorithm independently discovered by Roy and Warshall, which is the reason it is associated with all three authors.
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