Patent ID: 7406047

Claim:
A method of computing shortest paths in a weighted graph having vertices and an adjacency matrix with memory resources and a processor comprising: (a) selecting integer weights; (b) carrying out a series of incrementations, an incrementation comprising finding a set of vertices to which one may arrive from a given set of vertices; (c) carrying out a series of decrementations, a decrementation comprising finding a set of vertices from which one may go to arrive to a given set of vertices; (d) causing the incrementations and decrementations to be carried out in any order; (e) transforming vectors of increments/decrements in paths, the paths making up set E 1 of the shortest paths in term of number of arcs or using a given number of arcs, N a ; (f) selecting n-uple of paths C of lowest cost among a set of paths E 1 ; (g) calculating N b =N a +1; (h) computing iteratively, while N b ≦W(C) the following steps: i. check among paths of length N a +1 if in existance, having a weight lower than W(C) and selecting among them C′ of lowest cost (if such a path does not exist, then C′=C); and ii. C=C′ and N b =N b 1; and (i) determining paths of lowest weight based on C.