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Concurrent Processing of Linearly Ordered Data Structures on Hypercube Multicomputers
September 1994 (vol. 5 no. 9)
pp. 898-911

The paper presents a simple and effective method for the concurrent manipulation oflinearly ordered data structures on hypercube systems. The method Is based on theexistence of an augmented binomial search tree, called the pruned binomial tree, rootedat any arbitrary processor node of the hypercube such that; every edge of the treecorresponds to a direct link between a pair of hypercube nodes; and the tree spans anyarbitrary sequence of n consecutive nodes containing the root, using a fanout of at most[log/sub 2/ n] and a depth of at most [log/sub 2/ n]+1. Search trees spanningnonoverlapping processor lists are formed using only local information, and can be usedconcurrently without contention problems. Thus, they can be used for performingoperations such as broadcast and merge simultaneously on sets with nonuniform sizes.Extensions of the tree to k-ary n-cubes and faulty hypercubes are presented.Applications of this concurrent data structure to low- and intermediate-level imageprocessing algorithms, and for dictionary operations involving multiple keys, are alsooutlined.

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Index Terms:
Index Termstree data structures; trees (mathematics); search problems; hypercube networks;parallel algorithms; parallel programming; distributed memory systems; concurrentprocessing; linearly ordered data structures; hypercube multicomputers; concurrentmanipulation; hypercube systems; augmented binomial search tree; pruned binomial tree;arbitrary processor node; consecutive nodes; fanout; search trees; nonoverlappingprocessor lists; local information; broadcast; merge; k-ary n-cubes; intermediate-levelimage processing algorithms; dictionary operations; low-level image processingalgorithms; concurrent data structure; Gray code embedding; distributed memorymulticomputers
Citation:
J. Ghosh, S.K. Das, A. John, "Concurrent Processing of Linearly Ordered Data Structures on Hypercube Multicomputers," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 9, pp. 898-911, Sept. 1994, doi:10.1109/71.308529
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