shortest-path

I'm trying to understand exactly how these algorithms work, but I have been unable to find a simple explanation. I would greatly appreciate it if someone could provide or point me to a description of these algorithms that is easier to understand than the description in the original papers. Thanks. Alma Rahat First of all let me provide you with the links to the papers you were talking about. Eppstein's paper: D. Eppstein, “Finding the k shortest paths,” SIAM J. Comput., vol. 28, no. 2, pp.652–673, Feb. 1999 Yen's paper: J. Y. Yen, “Finding the K Shortest Loopless Paths in a Network,”

Here is an excise: Let G be a weighted directed graph with n vertices and m edges, where all edges have positive weight. A directed cycle is a directed path that starts and ends at the same vertex and contains at least one edge. Give an O(n^3) algorithm to find a directed cycle in G of minimum total weight. Partial credit will be given for an O((n^2)*m) algorithm. Here is my algorithm. I do a DFS . Each time when I find a back edge , I know I've got a directed cycle. Then I will temporarily go backwards along the parent array (until I travel through all vertices in the cycle) and calculate the

I am reading up on Dijkstra's algorithm and the Floyd-Warshall algorithm. I understand that Dijkstra's finds the optimal route from one node to all other nodes and Floyd-Warshall finds the optimal route for all node pairings. My question is would Dijkstra's algorithm be more efficient than Floyd's if I run it on every single node in order to find the optimal route between all pairings. Dijkstra's runtime is O(E + VlogV) where Floyd's is O(V 3 ). If Dijkstra's fails, what would its runtime be in this case? Thanks! As others have pointed out, Floyd-Warshall runs in time O(n 3 ) and running a

I was revising single source shortest path algorithms and in the video, the teacher mentions that BFS/DFS can't be used directly for finding shortest paths in a weighted graph (I guess everyone knows this already) and said to work out the reason on your own. I was wondering the exact reason/explanation as to why it can't be used for weighted graphs. Is it due to the weights of the edges or anything else ? Can someone explain me as I feel a little confused. PS: I went through this question and this question. Consider a graph like this: A---(3)-----B | | \-(1)-C--(1)/ The shortest path from A to

Can any one tell me the difference between Dijkstra's and Prim's algorithms? I know what each of the algorithms do. But they look the same to me. Dijkstra's algorithm stores a summation of minimum cost edges whereas Prim's algorithm stores at most one minimum cost edge. Isn't this the same? Dijsktra's algorithm finds the minimum distance from node i to all nodes (you specify i). So in return you get the minimum distance tree from node i. Prims algorithm gets you the minimum spaning tree for a given graph . A tree that connects all nodes while the sum of all costs is the minimum possible. So

I'm trying build a method which returns the shortest path from one node to another in an unweighted graph. I considered the use of Dijkstra's but this seems a bit overkill since I only want one pair. Instead I have implemented a breadth-first search, but the trouble is that my returning list contains some of the nodes that I don't want - how can I modify my code to achieve my goal? public List<Node> getDirections(Node start, Node finish){ List<Node> directions = new LinkedList<Node>(); Queue<Node> q = new LinkedList<Node>(); Node current = start; q.add(current); while(!q.isEmpty()){ current =

I know that many algorithms are available for calculating the shortest path between two points in a graph or a grid, like breadth-first, all-pairs (Floyd's), Dijkstra's. However, as I noticed, all of these algorithms compute all the paths in that graph or grid, not only those between the two points we are interested in. MY QUESTION IS: if I have a grid, i.e. a two dimensional array, and I'm interested in computing the shortest path between two points, say P1 and P2, and if there are restrictions on the way I can move on the grid (for example only diagonally, or only diagonally and upwards, etc