On the Number of Permutations Performable by Extra-Stage Multistage Interconnection Networks
IEEE Transactions on Computers
A high-speed interconnection paradigm and its applications to optical interconnection networks
A high-speed interconnection paradigm and its applications to optical interconnection networks
Permutation capability of optical multistage interconnection networks: 72
Journal of Parallel and Distributed Computing
An Optimal Algorithm for Permutation Admissibility to Multistage Interconnection Networks
IEEE Transactions on Computers
An Optimal O(NlgN) Algorithm for Permutation Admissibility to Extra-Stage Cube-Type Networks
IEEE Transactions on Computers
Optical multistage interconnection networks: new challenges and approaches
IEEE Communications Magazine
Space Division Architectures for Crosstalk Reduction in Optical Interconnection Networks
QoS-IP 2003 Proceedings of the Second International Workshop on Quality of Service in Multiservice IP Networks
The Data Vortex, an All Optical Path Multicomputer Interconnection Network
IEEE Transactions on Parallel and Distributed Systems
Fast reconfiguration algorithms for time, space, and wavelength dilated optical Benes networks
International Journal of Parallel, Emergent and Distributed Systems
On path dependent loss and switch crosstalk reduction in optical networks
Information Sciences: an International Journal
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Because signals carried by two waveguides entering a common switch element would generate crosstalk, a regular N × N multistage interconnection network (MIN) cannot be directly used as an optical switch between N inputs and N outputs in an optical network. A simple solution is to use a 2N × 2N cube-type MIN to provide the N × N connections, which needs a much larger hardware cost. A recent research proposed another solution, called the time-domain approach, that divides the N optical inputs into several groups such that crosstalk-free connections can be provided by an N × N regular MIN in several time slots, one for each group. Researchers studied this approach on Omega networks and defined the class set θ to be the set of N-permutations realizable in two time slots on an Omega network. They proved that the size of θ is larger than the size of class Ω, where Ω consists of all N-permutations admissible to a regular N × N (nonoptical) Omega network. This paper first presents an optimal O(N log N) time algorithm for identifying whether a given permutation belongs to class θ or not. Using this algorithm, this paper then proves an interesting result that the class θ is identical to the class Ω + 1 which represents the set of N-permutations admissible to a nonoptical N × N one-extra stage Omega network.