Routing Functions – an Effective Approach to Deriving One-to-Many Disjoint Paths

This paper introduces a new concept called routing functions, which have a close relation to one-to-many disjoint paths in networks. By using a minimal routing function, a maximal number of disjoint paths whose maximal length is minimized in the worst case can be constructed in the hypercube and the folded hypercube. The end nodes of the paths constructed for the hypercube are not necessarily distinct. As a byproduct, the strong Rabin number of the hypercube and the Rabin number of the folded hypercube are computed. The latter provides a solution to an open problem raised by Liaw and Chang. A maximal number of disjoint paths whose total length is minimized can also be constructed in the hypercube by the use of a routing function.