Abstract

Formulas are presented for the transformation of three-dimensional shuffle patterns into the two-dimensional domain. The results are applied to the transformation of the interstage patterns of three-dimensional multistage interconnection networks into their isomorphic two-dimensional patterns (and vice versa). This paper explains material in J. Giglmayr, “Classification scheme for 3-D shuffle interconnection patterns,” Appl. Opt. 28, 3120–3128 (1989) and corrects some algebraic results.

© 1992 Optical Society of America

d-Dimensional (d ≥ 3) shuffle interconnections

Josef Giglmayr
Appl. Opt. 31(11) 1695-1708 (1992)

Classification scheme for 3-D shuffle interconnection patterns

Josef Giglmayr
Appl. Opt. 28(15) 3120-3128 (1989)

Basic building blocks for the switch-preserving transformation of shuffle interconnections

Josef Giglmayr
Appl. Opt. 32(26) 4992-5001 (1993)

Generation and evaluation of d-dimensional (d ≥ 3) optical shuffle patterns

Josef Giglmayr
Appl. Opt. 31(23) 4662-4675 (1992)

Three-dimensional Omega networks for optical implementation

L. Cheng and A. A. Sawchuk
Appl. Opt. 31(26) 5468-5479 (1992)