On 4/13/11 8:11 PM, Shaun Jackman wrote:
Hi,
I would like to find the longest path from vertex u to vertex v through a directed graph with positive edge weights. I know that u and v are choke points in the graph, in that if you start from vertex u and start following random edges, you will end up at vertex v in pretty short order. Is dijkstra_shortest_paths the best function for this purpose?
The vertices reachable from u without travelling through v form a small subgraph of the total graph. I want to avoid exploring beyond v, and I definitely don't need to know the distances to vertices beyond v.
Cheers, Shaun
Thinking about this a bit, to find the LONGEST length will by necessity require every path, because there is no way to trim a set of paths and say they can't be longer then the current longest. Shortest finding algorithms can trim the search space since once you get from u to a in distance d, once your current path is bigger than d you don't need to check going through a anymore. Since you say it forms a small DAG, a quick depth first search, keeping track of the longest path may be best. -- Richard Damon