A method for analyzing combinatorial properties of static connecting topologies

Abstract

The mathematical method which allows examining the possibility of a conflict — free realization of a given permutation by a static interconnection network has been developed. The method is based on the use of the congruence notion of the number theory. The method was used to examine the possibility of a conflict-free realization of such well-known permutations as perfect shuffle, cyclic shift, bit reversal and flip permutation by a binary hypercube and by a two-dimensional mesh with the use of common routing algorithms. Moreover a hypercube combinatorial properties were explored under two modes of the same routing algorithm: synchronous and asynchronous. It was shown that using of an asynchronous mode of routing in a hypercube enhances its permutation capabilities.

Supported by Russian Foundation for Basic Research, Project No. 94-01-01650