Optimal simulation of linear array and ring architectures on multiply-twisted hypercube

Abstract

The authors consider the problem of simulating linear arrays and ring architectures on a multiply twisted hypercube. For the hypercube, a powerful tool for embedding linear arrays and rings is the Gray code (GC), which cannot be directly applied to multiply twisted hypercubes. They define a new concept of reflected link label sequence and use it to define a generalized Gray code (GCC). It is shown that by using the GCC at least n-factorial distinct Hamiltonian paths and at least n-factorial/2+(n-2)-factorial distinct Hamiltonian cycles of Q/sub n//sup MT/ can be identified. A method is described for embedding a ring of an arbitrary number of modes into Q/sub n//sup MT/ with dilation 1 and congestion 1. This method can be extended to embed many mode-disjoint and link-disjoint rings of different sizes into Q/sub n//sup MT/ simultaneously.<>