BELLMAN_FORD
All-to-One Shortest Distances on Directed Graph

BELLMAN_FORD, a MATLAB library which implements the Bellman-Ford algorithm for finding the shortest distance from a given node to all other nodes in a directed graph whose edges have been assigned real-valued lengths.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

BELLMAN_FORD is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

DIJKSTRA, a MATLAB library which implements a simple version of Dijkstra's minimum distance algorithm for graphs.

FLOYD, a MATLAB library which implements Floyd's algorithm for finding the shortest distance between pairs of nodes on a directed graph.

TOMS097, a MATLAB library which computes the distance between all pairs of nodes in a directed graph with weighted edges, using Floyd's algorithm.

Reference:

1. Richard Bellman,
   On a routing problem,
   Quarterly of Applied Mathematics,
   Volume 16, 1958, pages 87-90.
2. Lester Ford,
   Network Flow Theory,
   RAND Corporation Paper P-923, 1956.

Source Code:

• bellman_ford.m, finds shortest paths from a given vertex of a weighted directed graph.
• i4mat_transpose_print.m, prints an I4MAT, transposed.
• i4mat_transpose_print_some.m, prints some of an I4MAT, transposed.
• i4vec_print.m, prints an I4VEC.
• r8vec_print.m, prints an R8VEC.
• timestamp.m, prints the current YMDHMS date as a time stamp.

Examples and Tests:

• bellman_ford_test.m, a sample calling program.
• bellman_ford_test01.m, solves a small problem with 6 nodes and 10 edges.
• bellman_ford_test.txt, the output file.

You can go up one level to the MATLAB source codes.