Continuous routing and batch routing on the hypercube
PODC '86 Proceedings of the fifth annual ACM symposium on Principles of distributed computing
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Optimum Broadcasting and Personalized Communication in Hypercubes
IEEE Transactions on Computers
Optimal communication algorithms for hypercubes
Journal of Parallel and Distributed Computing
The efficiency of greedy routing in hypercubes and butterflies
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Routing and performance evaluation in interconnection networks
Routing and performance evaluation in interconnection networks
Theory, Volume 1, Queueing Systems
Theory, Volume 1, Queueing Systems
Dynamic Broadcasting in Parallel Computing
IEEE Transactions on Parallel and Distributed Systems
A Trip-Based Multicasting Model in Wormhole-Routed Networks with Virtual Channels
IEEE Transactions on Parallel and Distributed Systems
Routing Schemes for Multiple Random Broadcasts in Arbitrary Network Topologies
IEEE Transactions on Parallel and Distributed Systems
Embedding and Reconfiguration of Spanning Trees in Faulty Hypercubes
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Computers
Multi-Node Multicast in Three and Higher Dimensional Wormhole Tori and Meshes with Load Balance
ICPP '00 Proceedings of the Proceedings of the 2000 International Conference on Parallel Processing
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The authors analyze the problem in which each node of the binary hypercubeindependently generates packets according to a Poisson process with rate lambda ; eachof the packets is to be broadcast to all other nodes. Assuming unit packet length and noother communications taking place, it is observed that the system can be stable insteady-state only if the load factor rho identical to lambda (2/sup d/-1)/d satisfies rho1 where d is the dimensionality (diameter) of the hypercube. Moreover, the authorsestablish some lower bounds for the steady-state average delay D per packet and deviseand analyze two distributed routing schemes that are efficient in the sense that stabilityis maintained for all rho rho * where rho * does not depend on the dimensionality d ofthe network, while the average delay D per packet satisfies Dor=Kd(1+ rho ) for smallvalues of rho (with constant K). The performance evaluation is rigorous for one scheme,while for the other the authors resort to approximations and simulations.