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Modified Dijsktra's Algorithm to return all paths that tie for shortest

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A modification of code published by Jorge Barrera to return all paths that tie for shortest path.

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Description

This code is heavily based on code published by Jorge Barrera, to the point that I have chosen to include his original documentation along with my own. His original code is linked below.

I produced this modification because I found that no implementation of Dijkstra's Algorithm available on Mathworks File Exchange would return multiple paths that tie for shortest. I have debugged this modification using several small networks, and I believe it works, but I have not yet tested it against large networks so I cannot promise that it is entirely bug-free.

In my additional documentation, you will see that I attempted, unsuccessfully, to further modify the code so that costs are computed through probabilistic addition instead of arithmatic addition (e.g. cost of moving along edges e1 and e2 = 1 - (1-coste1)(1-coste2, instead of e1+e2). I'd greatly appreciate any help that you can offer me to modify the code in this manner.

Acknowledgements

Dijkstra Very Simple inspired this file.

Required Products MATLAB
MATLAB release MATLAB 7.8 (R2009a)
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