# shortest path

(classic problem)

Definition: The problem of finding the shortest path in a graph from one vertex to another. "Shortest" may be least number of edges, least total weight, etc.

Also known as single-pair shortest-path problem.

Note: The problem is to find the weight of the shortest path. For a map, it is to produce the (shortest) road distance from one city to another city, not which roads to take.

A modification to most algorithms finds the shortest path, too. In predecessor[i][j] save the immediate predecessor of the shortest path from i to j. Suppose predecessor[i][j] is k; then the shortest path ends with … → k → j. If predecessor[i][k] is p, the shortest path ends with … → p → k → j. Continue working backward until you reach i.

Author: PEB

## Implementation

(C, C++, Pascal, Fortran, and Mathematica)
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 2 November 2020.
HTML page formatted Mon Nov 2 12:36:42 2020.

Cite this as:
Paul E. Black, "shortest path", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 2 November 2020. (accessed TODAY) Available from: https://www.nist.gov/dads/HTML/shortestpath.html