A self-routing permutation network
Journal of Parallel and Distributed Computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
On a Class of Rearrangeable Networks
IEEE Transactions on Computers
Fast Self-Routing Permutation Switching on an Asymptotically Minimum Cost Network
IEEE Transactions on Computers
A New Routing Algorithm for a Class of Rearrangeable Networks
IEEE Transactions on Computers
Bit-permute multistage interconnection networks
Microprocessing and Microprogramming
An engineering approach to computer networking: ATM networks, the Internet, and the telephone network
On the Correctness of Inside-Out Routing Algorithm
IEEE Transactions on Computers
Permutation Realizability and Fault Tolerance Property of the Inside-Out Routing Algorithm
IEEE Transactions on Parallel and Distributed Systems
Journal of the ACM (JACM)
Permutation capability of optical multistage interconnection networks: 72
Journal of Parallel and Distributed Computing
Interconnection Networks: An Engineering Approach
Interconnection Networks: An Engineering Approach
A Fast VLSI-Efficient Self-Routing Permutation Network
IEEE Transactions on Computers
nD-dBPN: New Self-Routing Permutation Networks Based On the de Bruijn Digraphs
ICPP '98 Proceedings of the 1998 International Conference on Parallel Processing
On the speedup required for combined input- and output-queued switching
Automatica (Journal of IFAC)
HiPC'05 Proceedings of the 12th international conference on High Performance Computing
Designing scalable WDM optical interconnects using predefined wavelength conversion
NETWORKING'06 Proceedings of the 5th international IFIP-TC6 conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communications Systems
Analyzing permutation capability of multistage interconnection networks with colored Petri nets
Information Sciences: an International Journal
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Hi-index | 14.98 |
The Benes network has been used as a rearrangeable network for over 40 years, yet the uniform N(2 \log N-1) control complexity of the N \times N Benes is not optimal for many permutations. In this paper, we present a novel O(\log N) depth rearrangeable network, called KR-Benes, that is permutation-specific control-optimal. The KR-Benes routes every permutation with the minimal control complexity specific to that permutation and its worst-case complexity for arbitrary permutations is bounded by the Benes; thus, it replaces the Benes when considering control complexity/latency. We design the KR-Benes by first constructing a restricted 2 \log K +2 depth rearrangeable network called K{\hbox{-}}{\rm Benes} for routing K{\hbox{-}}{\rm bounded} permutations with control 2N \log K, 0 \leq K \leq N/4. We then show that the N \times N Benes network itself (with one additional stage) contains every K{\hbox{-}}{\rm Benes} network as a subgraph and use this property to construct the KR-Benes network. With regard to the control-optimality of the KR-Benes, we show that any optimal network for rearrangeably routing K{\hbox{-}}{\rm bounded} permutations must have depth 2 \log K + 2 and, therefore, the K{\hbox{-}}{\rm Benes} (and, hence, the KR-Benes) is optimal.