Am 21.03.20 um 17:44 schrieb Franco Peschiera: > Since I could potentially do many iterations (and samplings), I would > like to have an unbiased sampling method for the Y paths without having > to enumerate them all. > > One option is to do the sampling during the construction of the paths. I > have in mind to just use the |get_out_neighbors| method on the start > node to do my own depth-first search, randomly choosing a neighbor at > each moment until I get to the |cutoff| or the end node. This, I could > do for each path until I get to my limit of paths to sample. I’m not > sure, though, if this is 1) similar in logic to the |all_paths| method > and 2) if this is close in efficiency (due to using python to iterate > and sample instead of C++).
This would be heavily biased. It could be that there are many more paths that go through one of the neighbors, so if you want sample uniformly from all paths, you have to do a weighted sample of the neighbors at each step. And these weights would change at each step. > Another option, although a lot more far-fetched, is to create my own > |all_paths| method in C++ and re-compile my own version of graph-tool. > Is this realistic? The problem here is not which language should be used. > Are there better options to doing this? Counting all paths between two nodes is conjectured to be NP-Hard. This is also known as the self-avoiding-walk (SAW) problem. Sampling SAWs is not straightforward either, I believe most efficient approaches are based on MCMC. I recommend you to study the literature a little bit before attempting a solution. (It would be a lot simpler if you would be seeking instead to sample *shortest* paths between two nodes. This can be done in linear time, is even implemented in graph-tool already in random_shortest_path().) Best, Tiago -- Tiago de Paula Peixoto <ti...@skewed.de>
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