On generalized diameters of interconnection networks

The authors study the generalized diameters for many existing networks for parallel computations, such as trees, hypercubes, meshes and butterflies. The generalized diameter, called the i-ameter and denoted by d_i(G), of a graph G=(V,E) is the length of the shortest Steiner tree that can be established between any i nodes in G. This generalized notion of diameter allows the computation of the communication cost for any number of nodes, in a given network. Exact values of the i-ameter are computed for complete binary trees and the k-ary trees. For other networks, exact values of i -ameter are given for smaller values of i, and bounds are given for higher values