Hello again Tiago, First of all thanks for the resources and help. As you may expect, I somewhat lack a specialized background in graph theory and so I sometimes miss the correct terminology. As a reminder, this is a DAG. I haven’t, yet, implemented the random unbiased generator version of all_paths you kindly shared in those links, although I have it listed as a possible future step. As a temporary workaround, I’ve been doing the following each time I want to randomly sample paths between two nodes: 1. I calculate the min and max length of paths between the two nodes (the min using topology.shortest_distance, a good aproximation of the max is trivial). 2. I sample a number between those min and max`. 3. I execute topology.all_paths with that number as cutoff argument to obtain the paths generator. 4. I then execute some sampling from that generator, with an iteration limit. This is, of course, just a very crude and biased way of sampling, but at least it returns a different set of paths at each time it is executed. Until now, I’ve been assuming each edge has a weight of 1. I now would like to test giving edges a weight in order for that cutoff argument to use it. I know the shortest_distance function accepts weights of edges in order to do Dijkstra. Could the same be done with all_paths such that the search is stopped if an accumulated weighted-distance is reached? Is there any (alternative) way of controlling which paths I get from the all_paths besides that cutoff argument? Or whatever specialized logic regarding path sampling / filtering I would have to implemented myself (just like the examples you shared)? Would this be something you would consider adding to graph-tool? For example, I’ve been even wondering if I could just create a temporal view from the graph, by a randomly filtering edges or nodes before samplinh the paths, so as to, again, reduce the graph I will be sampling at each iteration. as always thanks for your time and help! Franco Peschiera Message: 2
Date: Mon, 23 Mar 2020 21:37:52 +0000 From: Tiago de Paula Peixoto <tiago@skewed.de> To: Main discussion list for the graph-tool project <graph-tool@skewed.de> Subject: Re: [graph-tool] efficient random sampling of paths between two nodes Message-ID: <e7b73784-607d-6644-f613-46af6d9bc1d1@skewed.de> Content-Type: text/plain; charset=utf-8
Am 23.03.20 um 22:14 schrieb Franco Peschiera:
Hello Tiago,
First of all, thanks for your time.
I see what you mean by having a biased logic that would prefer shorter paths to longer ones, I had not thought about that.
Regarding the self-reference part, I think it would not be a problem because of the structure of my particular (directed) graph. In fact, each node represents an assignment *at some given time period* and the outward neighbors of a node represent assignments *in the future*. In this way, a path can never visit a previously visited node since there are no possible cycles. In fact I can easily calculate the shortest and longest possible path between two nodes (shortest: using graphql's `shortest_distance` method, longest= number of periods in between the two nodes).
Well, for DAG (directed acyclic graphs) the situation is quite different, you should have said so in the beginning.
So the paths I want to create (or sample) are just the different ways one can go from a node N1 (in period P1) to node N2 (in period P2 > P1).? I think that in my graph I could just sample neighbors with a weight that depends on how far they are (in number of periods) from the node: the farthest neighbor will have the least probability of being chosen. This way, I'd compensate the fact that shorter paths take less hops.
What do you think?
Why do I get the impression I'm using google more than you to answer your question?
Here is an approach using rejection sampling:
https://math.stackexchange.com/questions/2673132/a-procedure-for-sampling-pa...
Another approach is to count the number of paths that go through each node (this is feasible for DAGs) and use this to sample directly, see:
https://pdfs.semanticscholar.org/0d74/e82c41124f83c842d5432abcb914ed1f410f.p...
Best, Tiago
-- Tiago de Paula Peixoto <tiago@skewed.de>