single-source shortest-path problem

(classic problem)

Definition: Find the shortest paths from a specific source vertex to every other vertex in a weighted, directed graph. Dijkstra's algorithm solves this if all weights are nonnegative. The Bellman-Ford algorithm handles any weights.

See also graph, all pairs shortest path, single-destination shortest-path problem, DAG shortest paths, shortest path.

Note: Equivalent to the single-destination shortest-path problem with all directions reversed.

Author: PEB


See implementations at graph. Single-source shortest directed path (Java) from Sedgewick and Wayne "Algorithms" 4th edition.
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 15 October 2021.
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Cite this as:
Paul E. Black, "single-source shortest-path problem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 15 October 2021. (accessed TODAY) Available from: