"All Pairs Shortest Path" Graph Solver

Gives the shortest node-to-node distance along the edges of a graph for all node combinations.

Description

ALLSPATH - solve the All Pairs Shortest Path problem

Rapidly returns the shortest node-to-node distance along the edges of a graph, for all nodes in the graph.

USAGE: B = allspath(A)

A = input distance matrix between nodes

B = shortest path distance matrix between all nodes

Notes:
(1) For a graph with n nodes, A is an n-by-n distance matrix giving the distances between adjacent nodes. Since the distance from point i to point j is the same as the distance from point j to point i, A must be a symmetric matrix
(2) The distance from a node to itself can either be entered as zero or infinity. (Either will produce a correct result.) This means that the diagonal elements of the matrix A must all be either zero or infinity.
(3) The distance between nodes that are not adjacent to each other must be entered as either zero or infinity. (Either will produce a correct result.) This means that the (i,j) and (j,i) elements of A, where i and j are non-adjacent nodes, must all be either zero or infinity.
(4) If the input graph is not "connected," meaning that some nodes cannot be reached from other nodes no matter how many edges are traversed, then the distances between nodes that cannot be connected will be returned as infinite.
(5) Distances between a node and itself are returned as zero.
(6) This function codifies an original algorithm created by the author.
(7) No warranties; use at your own risk.
(8) Written by Michael Kleder, October 2005.

• Acknowledgements: This submission has inspired the following:; Advanced Dijkstra's Minimum Path Algorithm
• MATLAB release: MATLAB 7.0.4 (R14SP2)

[LIU Jerry]

It is indeed useful for my research!

[giuseppe d]

But what happens it the graph is not undirected? I think it doesn't work...

[giuseppe d]

There are a limit whenever we have a large graph. Out of memory proble...
Somebody tried?
G

[Kyaw Tun]

It give out of memory error even though my graph has only 702 nodes. :-)

[Dead Beat]

Doesn't work, fails with a "??? Out of memory. Type HELP MEMORY for your options." even tho my graph has 600 nodes & I have 1GB of RAM!

[David Leamer]

What a beautifully compact algorithm! Works fast for up to about 200-250 nodes. For more than that it works but uses a lot of memory. This is really*great for smallish (about 200 nodes) investigational type problems that I'm working on right now.

[John S]

Works great for me, < 200-ish nodes. Thanks!

[Joseph Kirk]

The example didn't work for me...
??? Undefined function or method 'pdist' for input arguments of type 'double'.
Do I need a special toolbox for this?

[The Author]

Thank you. PDIST does require the Statistics Toolbox, so I have removed it from the example and uploaded a replacement submission where the example does not use PDIST.

[Joseph Kirk]

Thank you for putting in the effort to update the file with the new example for those of us lacking the Statistics Toolbox. :)

However, I still had some difficulty testing it. References were made to variables 'a' and 'b' that did not exist. I was able to run the example when I added the following code after "% distance matrix:"

>> k=(1:10); a=k(ones(1,10),:); b=a';