Equivalence of multistage interconnection networks
Information Processing Letters
Optimum Broadcasting and Personalized Communication in Hypercubes
IEEE Transactions on Computers
All-to-All Personalized Communication in a Wormhole-Routed Torus
IEEE Transactions on Parallel and Distributed Systems
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
Optimal All-to-All Personalized Exchange in a Class of Optical Multistage Networks
IEEE Transactions on Parallel and Distributed Systems
All-To-All Communication with Minimum Start-Up Costs in 2D/3D Tori and Meshes
IEEE Transactions on Parallel and Distributed Systems
Efficient All-to-All Personalized Exchange in Multidimensional Torus Networks
ICPP '98 Proceedings of the 1998 International Conference on Parallel Processing
Optimal All-to-All Personalized Exchange in Multistage Networks
ICPADS '00 Proceedings of the Seventh International Conference on Parallel and Distributed Systems
One-to-all personalized communication in torus networks
PDCN'07 Proceedings of the 25th conference on Proceedings of the 25th IASTED International Multi-Conference: parallel and distributed computing and networks
Logic programming for combinatorial problems
Artificial Intelligence Review
All-to-all personalized exchange in generalized shuffle-exchange networks
Theoretical Computer Science
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In parallel/distributed computing systems, the all-to-all personalized communication (or complete exchange) is required in numerous applications of parallel processing. In this paper, we consider this problem for logN stage Multistage Interconnection Networks (MINs). It is proved that the set of admissible permutations for a MIN can be partitioned in Latin Squares. Since routing permutations belonging to a Latin Square provides the all-to-all personalized communication, a method to realize the complete exchange with time complexity O(N), that is optimal, can be derived. This method, compared with other ones in literature, does not necessitate of neither pre-computation nor memory allocation to record the Latin Square, because an explicit construction of it is not required; furthermore it is applicable to any logN stage multistage networks since it is independent of the topology.