shortest-path

I am implementing a symmetric bidirectional A* shortest path algorithm, as mentioned in [Goldberg and Harrelson,2005] . This is only for understanding the algorithm, therefore I used the most basic version without any optimization steps. My problem is the bidirectional algorithm appears to scan almost two times the number of edges scanned in a uni-directional A* search on the test graph. Example: a s-t query on a road network using A* (left) and bidirectional A* (right). Nodes scanned by the forward and backward search are colored in red and green, respectively. The heuristic function is

Given a directed graph G=(V,E) , two vertices s , t and two weight functions w1 , w2 , I need to find the shortest path from s to t by w2 among all the shortest paths between s to t by w1 . First of all , how could I find all the shortest paths between two vertices s and t ? Dijkstra's algorithm helps us find shortest path from a vertex to to every other accessible vertex, is it possible to modify it in order to get all the shortest paths between two vertices? I will expand on comments to the question. The problem is, for some graphs, you can have an exponential number of shortest paths

I've successfully implemented Bellman-Ford to find the distance of the shortest path when edges have negative weights/distances. I've not been able to get it to return all shortest paths (when there are ties for shortest). I managed to get all shortest paths (between a given pair of nodes) with Dijkstra. Is this possible with Bellman-Ford? (just want to know if I'm wasting my time trying) If you alter the second step of the Bellman-Ford algorithm a little bit you can achieve something very similar: for i from 1 to size(vertices)-1: for each edge uv in edges: // uv is the edge from u to v u :=

Go, Dijkstra : print out the path, not just calculate the shortest distance. http://play.golang.org/p/A2jnzKcbWD I was able to find the shortest distance using Dijkstra algorithm, maybe not. The code can be found here. But it would be useless if I can't print out the path. With a lot of pointers going on, I can't figure out how to print out the final path that takes the least amount of weights. In short, how do I not only find the shortest distance, but also print out the shortest path on this given code? The link is here: http://play.golang.org/p/A2jnzKcbWD And the snippet of the code is

I have implemented a simple Dijkstra's algorithm for finding the shortest path on an .osm map with Java. The pathfinding in a graph which is created from an .osm file works pretty well. But in case the user's current location and/or destination is not a node of this graph (just raw coordinates) how do we 'link' those coordinates to the graph to make pathfinding work? The simple straightforward solution "find the nearest to the current location node and draw a straight line" doesn't seem to be realistic. What if we have a situation like on the attached picture? (UPD) The problem here is that

In a directed graph with non-negative edge weights I can easily find shortest path from u to v using dijkstra's. But is there any simple tweak to Dijkstra's so that I can find shortest path from u to v through a given vertex w. Or any other algorithm suggestions? Find the shortest path from u to w, then the shortest path from w to v. Find shortest path from u to w Find shortest path from w to v Then u->w->v is the shortest path. You can do it by running Dijkstra for two times, but you can also apply the Floyd-Warshall algorithm. Zach Langley This problem is NP-hard, so finding a polynomial