graph-algorithm

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,”

If you have a graph, and need to find the diameter of it (which is the maximum distance between two nodes), how can you do it in O(log v * (v + e)) complexity. Wikipedia says you can do this using Dijkstra's algorithm with a binary heap . But I don't understand how this works. Can someone explain please? Or show a pseudocode? For a general Graph G=(V,E) there is no O(log V * (V + E)) time complexity algorithm known for computing the diameter. The current best solution is O(V*V*V) , e.g., by computing all shortest Paths with Floyd Warshall's Algorithm. For sparse Graphs, i.e. when E is in o(N*N

I'm working on a homework problem that asks me this: Tiven a finite set of numbers, and a target number, find if the set can be used to calculate the target number using basic math operations (add, sub, mult, div) and using each number in the set exactly once (so I need to exhaust the set). This has to be done with recursion. So, for example, if I have the set {1, 2, 3, 4} and target 10, then I could get to it by using ((3 * 4) - 2)/1 = 10. I'm trying to phrase the algorithm in pseudo-code, but so far haven't gotten too far. I'm thinking graphs are the way to go, but would definitely

Prim's and Kruskal's algorithms are used to find the minimum spanning tree of a graph that is connected and undirected. Why can't they be used on a graph that is directed? It's a minor miracle that these algorithms work in the first place -- most greedy algorithms just crash and burn on some instances. Assuming that you want to use them to find a minimum spanning arborescence (directed paths from one vertex to all others), then one problematic graph for Kruskal looks like this. 5 --> a / / ^ s 1| |2 \ v / --> b 3 We'll take the a->b arc of cost 1, then get stuck because we really wanted s->b

I'm looking for a simple algorithm to 'serialize' a directed graph. In particular I've got a set of files with interdependencies on their execution order, and I want to find the correct order at compile time. I know it must be a fairly common thing to do - compilers do it all the time - but my google-fu has been weak today. What's the 'go-to' algorithm for this? Andrew Peters Topological Sort (From Wikipedia): In graph theory, a topological sort or topological ordering of a directed acyclic graph (DAG) is a linear ordering of its nodes in which each node comes before all nodes to which it has

I have an undirected, positive-edge-weight graph (V,E) for which I want a minimum spanning tree covering a subset k of vertices V (the Steiner tree problem). I'm not limiting the size of the spanning tree to k vertices; rather I know exactly which k vertices must be included in the MST. Starting from the entire MST I could pare down edges/nodes until I get the smallest MST that contains all k . I can use Prim's algorithm to get the entire MST, and start deleting edges/nodes while the MST of subset k is not destroyed; alternatively I can use Floyd-Warshall to get all-pairs shortest paths and