NIST

all pairs shortest path

(classic problem)

Definition: Find the weight (or length) of the shortest paths between all pairs of vertices in a weighted, directed graph.

See also Floyd-Warshall algorithm, Johnson's algorithm similar problems: single-source shortest-path problem, shortest path, minimum spanning tree, traveling salesman, all simple paths.

Note: The problem is to find the weights of the shortest paths between all pairs of vertices. For a map, it is to produce the (shortest) road distances between all cities, not which roads to take to get from one city to another.

After LK.

Author: PEB

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 1 February 2005.
HTML page formatted Wed Mar 13 12:42:45 2019.

Cite this as:
Paul E. Black, "all pairs shortest path", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 1 February 2005. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/allPairsShortestPath.html