Classification scheme for 3-D shuffle interconnection patterns

Abstract

Two different types of the generalized perfect shuffle (GPS) and the generalized inverse shuffle (GIS) are considered in this paper: the standard symmetric GPS and GIS where a common basis exists for the numbering of both coordinates of the data array and the nonsymmetric GPS and GIS where each coordinate has a different basis. Additionally, the GPS is combined with the GIS providing the generalized mixed shuffle pattern. These shuffle patterns are transformed into their isomorphic 2-D counterparts and classified with respect to the number of standard perfect shuffle steps obtained by factorizing the permutations.

© 1989 Optical Society of America

d-Dimensional (d ≥ 3) shuffle interconnections

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

Transformation of three-dimensional shuffle patterns

Josef Gigimayr
Appl. Opt. 31(11) 1709-1716 (1992)

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)

Organization of k × k switches (k ≥ 4) interconnected by d-dimensional (d ≥ 2) regular optical patterns

Josef Giglmayr
Appl. Opt. 30(35) 5119-5135 (1991)