[gk101]

A few comments just in case this a critical part of your program, and if running it faster would help:

1. Using a heap with Dijkstra's algorithm would speed up your program

From your comment I am guessing you are using Dijkstra's algorithm without a heap, which gives O(n * m) for one source, and O(n^2 * m) for all sources (all pairs shortest path), where n is the number of nodes/vertices, and m is the number of edges

You would be able to improve that to O(m * n * lgn) by using a heap, which improves the time to run it by quite a lot in practice

2. The time it takes to run the program also depends on the density of your matrix:

In the case where the graph is sparse: m ~ n, and will result in O(n^2 * lgn) (or O(n^3) without a heap)

In the case where the graph is dense: m ~ n^2, and will result in O(n^3 * lgn) (or O(n^4) without a heap)

Compare the numbers above to O(n^3), which is the time complexity of Floyd-Warshall

So just in terms of time complexity, Floyd-Warshall would be faster in a dense graph

[R_haterade]

Agreed, but this was for a fast script that will probably run 100 times for analysis purposes--the code itself wasn't the end goal. I just needed something that could crunch my numbers in 10 minutes instead of 2 hours. :-)

[R_haterade]

I do want to express that I appreciate the effort you put into this post. Algorithms and data structures are my weakest point right now, and being able to read through your explanation is a helpful thing.