Shortest path problem - Wikipedia, the free encyclopedia

Shortest path problem - Wikipedia, the free encyclopedia -...

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Unformatted text preview: Shortest path problem - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Shortest_path_problem 1 of 2 12/13/2006 1:59 PM Shortest path problem From Wikipedia, the free encyclopedia In graph theory, the single-source shortest path problem is the problem of finding a path between two vertices such that the sum of the weights of its constituent edges is minimized. More formally, given a weighted graph (that is, a set V of vertices, a set E of edges, and a real-valued weight function f : E → R ), and given further one element v of V , find a path P from v to each v' of V so that is minimal among all paths connecting v to v' . The all-pairs shortest path problem is a similar problem, in which we have to find such paths for every two vertices v to v' . A solution to the shortest path problem is sometimes called a pathing algorithm . The most important algorithms for solving this problem are: Dijkstra's algorithm — solves single source problem if all edge weights are greater than or equal to zero. WithoutDijkstra's algorithm — solves single source problem if all edge weights are greater than or equal to zero....
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