Abstract

With the increasing demand for solving computation-intensive tasks such as image processing and image understanding, a volume (3-D), dynamic multistage interconnection network that interconnects a 2-D array of channels to another is desirable.¹ The understanding of the properties of these networks and their relationships is important for constructing useful; 3-D networks. Here, we study the class of 3-D Omega networks based on different shuffling principles and arrangements of the switch elements. The results show that the 3-D Omega networks using 2-D folded shuffles combined with 2×2 bypass/exchange switch element arrays2 in the 2-D plane are either topologically identical or equivalent to 2-D Omega networks using 1-D perfect shuffles combined with 2×2 bypass/exchange switch element arrays. Networks using 2-D separable shuffles combined with 2×2 bypass/exchange switch element arrays are full access only for a particular arrangement of the switch element arrays at the stages. A reduced-state 4×4 switch element, formed by four 2×2 switch elements with one pair lying horizontally, the other pair standing vertically and a direct connection between the two pairs, can be used at each stage. When reduced-state 4×4 switch element arrays are used, 3-D Omega networks with 2-D folded shuffles and 2-D separable shuffles are topologically identical.

© 1991 Optical Society of America