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<p><b>Abstract</b>—The <it>tree communication</it> scheme was shown to be very efficient for global operations on data residing in the processors of a hypercube with time complexity of <it>O</it>(log<sub>2</sub><it>N</it>), where <it>N</it> is the number of processors. This communication scheme is very useful for many parallel algorithms on hypercube multiprocessors. If a problem can be divided into independent subproblems, each subproblem can first be solved by one of the processors. Then, the tree communication scheme is invoked to merge the subresults into the final results. All the algorithms for problems with this property can benefit from the tree communication scheme. We propose a more general and efficient tree communication scheme in this paper. In addition, we also propose fault-tolerant algorithms for the tree communication scheme, by exploiting the unique properties of the tree communication scheme. The computation and communication slowdown is small (< 2) under the effect of multiple link and/or node failures.</p>
Hypercube, failures, tree communication, uniform data distribution, fault-tolerance.

S. Kuo and Y. Leu, "A Fault-Tolerant Tree Communication Scheme for Hypercube Systems," in IEEE Transactions on Computers, vol. 45, no. , pp. 641-650, 1996.
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