dijkstra

dijkstra, an Octave code which implements the Dijkstra algorithm for finding the minimum distance from a given node of a weighted graph to all the other nodes.

The example graph handled by the program has 6 nodes and 8 links, each with a positive length:

    N0--15--N2-100--N3
      \      |     /
       \     |    /
        40  20  10
          \  |  /
           \ | /
            N1
            / \
           /   \
          6    25
         /       \
        /         \
      N5----8-----N4
      

Using "Inf" to indicate that there is no link between two nodes, the distance matrix for this graph is:

          0   40   15  Inf  Inf  Inf
         40    0   20   10   25    6
         15   20    0  100  Inf  Inf
        Inf   10  100    0  Inf  Inf
        Inf   25  Inf  Inf    0    8
        Inf    6  Inf  Inf    8    0
      

Dijkstra's algorithm efficiently determines the length of the shortest path from node 0 to other nodes as:

        From 0 to:  0    1    2    3    4    5
        Distance:   0   35   15   45   49   41
      

Licensing:

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

Languages:

dijkstra is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version

Related Data and Programs:

dijkstra_test

floyd, an Octave code which implements Floyd's algorithm for finding the shortest distance between pairs of nodes on a directed graph.

toms097, an Octave code which computes the distance between all pairs of nodes in a directed graph with weighted edges, using Floyd's algorithm.

Reference:

1. Edsger Dijkstra,
   A note on two problems in connexion with graphs,
   Numerische Mathematik,
   Volume 1, 1959, pages 269-271.

Source Code:

• dijkstra_distance.m, carries out Dijkstra's minimum distance algorithm.
• find_nearest.m, finds the nearest unconnected node.
• init.m, initializes the problem data.
• update_mind.m, updates the minimum distance vector.