Find best paths sorted by length with graph tools

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Find best paths sorted by length with graph tools

Franco Peschiera
Good day,

I can give some feedback on this since I've also used graph-tool for getting paths. In my case it was slightly different because (1) I wanted to sample paths without bias, (2) I used a weight on the arcs, (3) my arcs were directed and (4) the number of nodes and edges was really big . Sadly, (1) and (2) made it not very easy to do it via graph tool.

As far as I understand, graph tool uses a DFS to obtain `all_paths`. When the number of potential paths is large for a given cutoff but the remaining number of valid paths is small, it will iterate a long time (at each `next()`) until it proves there are no more paths that have a length equal or smaller to the cutoff.

You could choose to stop the iteration once it starts taking longer than certain time to find a path, but even this is no guarantee. There may be many paths still remaining to be found. You can also play with the number of paths to return...

Another thing you should take into account if you want to stop `all_paths` at a limit number of paths is that since it does a DFS, two paths that are close in the returned list will be "close" in structure (i.e., similar). So "sampling" paths this way is not great.

Sorry I cannot be of more help. If you find a better way to do it with graph-tool, please share it over here!

Good luck!

Franco



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   1. Find best paths sorted by length with graph tools (Ruhm)


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Message: 1
Date: Tue, 15 Dec 2020 08:22:24 -0700 (MST)
From: Ruhm <[hidden email]>
To: [hidden email]
Subject: [graph-tool] Find best paths sorted by length with graph
        tools
Message-ID: <[hidden email]>
Content-Type: text/plain; charset=us-ascii

Hello,

I'm a beginner in graph algorithm, and I have trouble to find an efficient
solution for my issue.

My goal is to find X best paths between two vertices. Not only the shortest
paths, but sub optimals path, ordered by length.
My graph is relatively small (10k vertices, 20k edges) and is not directed.
I don't use weight or vertices/edges attributes.

My current prototype:
I use first all_shortest_paths to find the best paths.
Then I use all_paths with a cutoff = length of shortest_path + K . K is an
arbitrary value set as an argument of my function.
Finally, I sort the return of all_paths by path length and select the X
shortest.

It works fine when the vertices are close to each other, but when my cutoff
is over 20ish, the all_paths function take forever and my CPU usage
skyrockets. I can't even iterate with next() over the result. I understand
that all_paths is not very effective in my case, but at the moment this is
my best guess.

I'm reading the documentation of graph tools, but I cant find any other
function fitting my needs. I 'm considering using the function bfs_search
with a custom BFSVisitor, but I'm afraid i will encounter performance issues
too.

Am i missing something?

Anyways, thanks for this library, its impressive.
Sorry for my poor English.

Regards



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