Communication effect basic linear algebra computations on hypercube architectures
Journal of Parallel and Distributed Computing
Optimal Broadcast in All-Port Wormhole-Routed Hypercubes
IEEE Transactions on Parallel and Distributed Systems
A near-optimal broadcasting algorithm in all-port wormhole-routed hypercubes
ICS '95 Proceedings of the 9th international conference on Supercomputing
Circuit-Switched Broadcasting in Torus Networks
IEEE Transactions on Parallel and Distributed Systems
Circuit-Switched Broadcasting in Torus and Mesh Networks
IEEE Transactions on Parallel and Distributed Systems
All-to-All Personalized Communication in a Wormhole-Routed Torus
IEEE Transactions on Parallel and Distributed Systems
A Broadcast Algorithm for All-Port Wormhole-Routed Torus Networks
IEEE Transactions on Parallel and Distributed Systems
A Dilated-Diagonal-Based Scheme for Broadcast in a Wormhole-Routed 2D Torus
IEEE Transactions on Computers
Concrete Math
ICCD '92 Proceedings of the 1991 IEEE International Conference on Computer Design on VLSI in Computer & Processors
CCL: A Portable and Tunable Collective Communication Library for Scalable Parallel Computers
Proceedings of the 8th International Symposium on Parallel Processing
Circuit-Switched Broadcasting in Multi-port Multi-dimensional Torus Networks
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Optimal broadcast in /spl alpha/-port wormhole-routed mesh networks
ICPADS '97 Proceedings of the 1997 International Conference on Parallel and Distributed Systems
Circuit-Switched Broadcasting in itd-Dimensional Tori and Meshes
Proceedings of the 8th International Symposium on Parallel Processing
A broadcast algorithm for all-port wormhole-routed torus networks
FRONTIERS '95 Proceedings of the Fifth Symposium on the Frontiers of Massively Parallel Computation (Frontiers'95)
Circuit-Switched Broadcasting in Multi-Port Multi-Dimensional Torus Networks
The Journal of Supercomputing
A New Conference Network for Group Communication
IEEE Transactions on Computers
A Recursion-Based Broadcast Paradigm in Wormhole Routed Mesh/Torus Networks
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
ISHPC '00 Proceedings of the Third International Symposium on High Performance Computing
Journal of Systems Architecture: the EUROMICRO Journal
Pipelining Broadcasts on Heterogeneous Platforms
IEEE Transactions on Parallel and Distributed Systems
A Recursion-Based Broadcast Paradigm in Wormhole Routed Networks
IEEE Transactions on Parallel and Distributed Systems
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The one-to-all broadcast is the most primary collective communication pattern in a multicomputer network. We consider this problem in a wormhole-routed torus which uses the all-port and dimension-ordered routing model. We derive our routing algorithms based on the concept of 驴span of vector spaces驴 in linear algebra. For instance, in a 3D torus, the nodes receiving the broadcast message will be 驴spanned驴 from the source node to a line of nodes, to a plane of nodes, and then to a cube of nodes. Our results require at most $2(k-1)$ steps more than the optimal number of steps for any square $k$-D torus. Existing results, as compared to ours, can only be applied to tori of very restricted dimensions or sizes and either rely on an undesirable non-dimension-ordered routing or require more numbers of steps.