# efficient random sampling of paths between two nodes

Hello Tiago,

Thanks again for the quick answers and feedback.

In fact, the more I think about how to take the most advantage of the
graph, the more I think that in my case what I would really like is to
control the way the paths are being sampled. So, the process would become a
biased sampling where I’m the one giving the bias in the form of the
probability of choosing each edge when traversing from the origin to the
destination. This probability would depend on information of the node and
additional information that will depend on each iteration of my algorithm.
It could also be an edge property, I guess.

One caveat is that DFS will not be possible since I want to make each
sampling independent from the previous one and so getting several paths
would be less efficient. Although I’d assume that this is not too much of a
problem given that I’d need a smaller sample if I know it’s probably going
to be a better one.

I was thinking on doing something on the lines of the following (I’ve only
tested it with a small graph):

def sample_path_from_nodes(node1, node2, all_weights, cutoff):
# all_weights is a dictionary on the graph edges
current = node1
path = []
visited = set()
while True:
if current == node2:
# we finished!
return path + [current]
neighbors = set(current.out_neighbors()) - visited
if len(path) >= cutoff or not len(neighbors):
# this path does not reach node2
# we backtrack
# and we will never visit this node again
current = path.pop()
continue
if not len(path) and not len(neighbors):
# there is no path to node2
# this should not be possible
return None
# we haven't reached node2
# but there is still hope
path.append(current)
weights = [all_weights.get((current, n), 1) for n in neighbors]
_sum = sum(weights)
weights = [w/_sum for w in weights]
current = np.random.choice(a=list(neighbors), p=weights)

I fear this will not be as efficient as just getting a lot of paths via
all_paths. Do you think this makes sense for sampling with preferences on
edges? And if so, do you think it will perform a lot better if I did it as
a graph-tool C++ extension? I guess I can always test the python version
and see how it goes…

thanks!

Franco

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I fear this will not be as efficient as just getting a lot of paths via
>all_paths|. Do you think this makes sense for sampling with preferences
on edges?

I'll refrain from judging whether it makes sense. It's up to you to
decide for yourself what you want to do.

And if so, do you think it will perform a lot better if I did
it as a graph-tool C++ extension?

In general C++ will speed up any equivalent algorithm when compared to
pure python, often by factors of up to 200x. But a good advice is to
focus first on defining your problem well, and writing a correct
implementation first, and worrying about optimization later.

Best,
Tiago