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From: Greg Link (link_at_[hidden])
Date: 2006-05-11 11:07:39

Dima -
        I've got a 2D grid-structure, of some size "n x n". Each point in
the grid is connected to it's four neighboring and adjacent cells in
the grid by an edge. The edges (and their weights) represent the
delay to travel between those two points in the grid. The weight of
the edges is non-uniform, and determined at run-time.
        I have a set of {X1,Y1} and {X2,Y2} pairs that I want to find the
shortest path between. The set is 'large'. Rather than running the
standard dijkstra_shortest_path, and therefore having a run-time of O
(num_pairs * V^2), I use johnson to find the all_pairs paths, at a
cost of O(V*E*log(V)). Since E=2*V, that's effectively (V^2 log(V)).
For any num_pairs > log(V), the johnson algorithm /should/ be faster.

        I do this a number of times (10 million), constructing a new graph
each time, putting the edges in, and then solving the all_pairs
paths. Profling the code shows that the graph construction is fairly
trivial compared to the actual johnson algorithm (and the BFS_Visitor
beneath that). Anything else that might help?

        Thanks for your interest,
- Greg

On May 11, 2006, at 10:53 AM, Dmitry Bufistov wrote:

> Greg Link wrote:
>> I'm using BGL for the johnson_all_pairs_shortest_path algorithm,
>> [snip]
>> and I'm wondering if that's the best choice. My graph has (E=2*V),
>> and all nodes are of constant degree, with 4 edges incident on them.
> Hi Grek,
> Probably there is better algorithm for your original problem).
> Could you
> describe in brief it?
> Regards,
> --dima
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