Optimization Of An All-paths Algorithm

I've been successful using the following algorithm to complete all-path data up to path length of 10 on graphs of ~900 nodes. However, I want to scale it up to larger graphs and I'

Solution 1:

First of all - measurement is your best friend. If you are not collecting information about how long the algorithm takes, then you have no real way of knowing if a change helps or not. Your idea to cache your results is clever, but you should check timings with and without the caching to make sure it actually helps.

One part of your code in particular that I can see room for improvement in is if (visited not in uniqueTreePaths).... You are checking to see if a list is contained in a list of lists. I'm not sure what the best way to fix this would be (again, collect timing data from your code), but one possibility would be to represent the paths as strings instead of lists, allowing them to be stored by hashes.