This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 singlesource 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 realvalued 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 allpairs 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....
View
Full Document
 Spring '10
 JenniferChen
 Graph Theory, Wikipedia, Shortest path problem, shortest path, Graph algorithms

Click to edit the document details