Journal of the ACM (JACM)
Parallel Processing with the Perfect Shuffle
IEEE Transactions on Computers
Notes on Shuffle/Exchange-Type Switching Networks
IEEE Transactions on Computers
Interconnections Between Processors and Memory Modules Using the Shuffle-Exchange Network
IEEE Transactions on Computers
The Universality of the Shuffle-Exchange Network
IEEE Transactions on Computers
The Indirect Binary n-Cube Microprocessor Array
IEEE Transactions on Computers
Parallel Permutations of Data: A Benes Network Control Algorithm for Frequently Used Permutations
IEEE Transactions on Computers
Access and Alignment of Data in an Array Processor
IEEE Transactions on Computers
A Shuffle-Exchange Network with Simplified Control
IEEE Transactions on Computers
A new interconnection network for SIMD computers: the sigma networks
IEEE Transactions on Computers
A journey into multicomputer routing algorithms
PAS '95 Proceedings of the First Aizu International Symposium on Parallel Algorithms/Architecture Synthesis
| Hi-index | 14.98 |
Let O denote the set of permutations performable by a pass through the Omega network (an n-stage shuffle-exchange network), and let p denote an arbitrary permutation of N = 2n elements. In this paper we characterize the sets {p|pO = O} (called left invariants) and {p|Op = O} (called right invariants). This characterization provides a useful criterion for determining whether or not the composition of two permutations belongs to O; it also allows a number of known results to be generalized and their derivations simplified.