Finite State Model and Compatibility Theory: New Analysis Tools for Permutation Networks
IEEE Transactions on Computers
Fast Self-Routing Permutation Switching on an Asymptotically Minimum Cost Network
IEEE Transactions on Computers
A New Self-Routing Permutation Network
IEEE Transactions on Computers
Wide-Sense Nonblocking Clos Networks Under Packing Strategy
IEEE Transactions on Computers
Permutation Realizability and Fault Tolerance Property of the Inside-Out Routing Algorithm
IEEE Transactions on Parallel and Distributed Systems
Optimal All-to-All Personalized Exchange in Self-Routable Multistage Networks
IEEE Transactions on Parallel and Distributed Systems
Permutation capability of optical multistage interconnection networks: 72
Journal of Parallel and Distributed Computing
Performing Permutations on Interconnection Networks by Regularly Changing Switch States
IEEE Transactions on Parallel and Distributed Systems
Optimal All-to-All Personalized Exchange in a Class of Optical Multistage Networks
IEEE Transactions on Parallel and Distributed Systems
Introductory Combinatorics
Interconnection Networks: An Engineering Approach
Interconnection Networks: An Engineering Approach
Reconfiguration with Time Division Multiplexed MIN's for Multiprocessor Communications
IEEE Transactions on Parallel and Distributed Systems
Wavelengths Requirement for Permutation Routing in All-Optical Multistage Interconnection Networks
IPDPS '00 Proceedings of the 14th International Symposium on Parallel and Distributed Processing
Efficient Protocols for Permutation Routing on All-Optical Multistage Interconnection Networks
ICPP '00 Proceedings of the Proceedings of the 2000 International Conference on Parallel Processing
Routing Permutations on Baseline Networks with Node-Disjoint Paths
IEEE Transactions on Parallel and Distributed Systems
High-Performance Self-Routing Algorithm for Multiprocessor Systems with Shuffle Interconnections
IEEE Transactions on Parallel and Distributed Systems
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In this paper, we consider efficiently routing permutations in a class of switch-based interconnects. Permutation is an important communication pattern in parallel and distributed computing systems. We present a generic approach to realizing arbitrary permutations in a class of unique-path, self-routable interconnects. It is well-known that this type of interconnect has low hardware cost, but can realize only a small portion of all possible permutations between its inputs and outputs in a single pass. In this paper, we consider routing arbitrary permutations with link-disjoint paths and node-disjoint paths in such interconnects in a minimum number of passes. In particular, routing with node-disjoint paths has important applications in the emerging optical interconnects. We employ and further expand the Latin square technique used in the all-to-all personalized exchange algorithms for this class of interconnects for general permutation routing. As can be seen, our implementation of permutation routing is optimal in terms of the number of passes that messages are transmitted through the network, and it is near-optimal in network transmission time for sufficiently long messages. The possibility of adopting a single-stage interconnect is also discussed.