Communication effect basic linear algebra computations on hypercube architectures
Journal of Parallel and Distributed Computing
The connection machine
Embedding meshes in Boolean cubes by graph decomposition
Journal of Parallel and Distributed Computing - Special issue: algorithms for hypercube computers
Combinatorial Algorithms: Theory and Practice
Combinatorial Algorithms: Theory and Practice
ROMM routing on mesh and torus networks
Proceedings of the seventh annual ACM symposium on Parallel algorithms and architectures
Mechanical Verification of Hypercube Algorithms
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
On fault-tolerant embedding of meshes and tori in a flexible hypercube with unbounded expansion
WSEAS TRANSACTIONS on SYSTEMS
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We present a new algorithm for conversion between binary code and binary-reflected Gray code that requires approximately 2 K/3 element transfers in sequence for K elements per node, compared to K element transfers for previously known algorithms. For a binary cube of n=2 dimensions the new algorithm degenerates to yield a complexity of 2 K/+1 element a transfers, which is optimal. The new algorithm is optimal to within a multiplicative factor of 4/3 with respect to the best known 3 lower bound for any routing strategy. We show that the minimum number of element transfers for minimum path length routing is K with concurrent communication on all channels of every node of a binary cube