Parallel Algorithms for the Classes of +or-2^b DESCEND and ASCEND Computations on a SIMD Hypercube
IEEE Transactions on Parallel and Distributed Systems
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Recently, the author has studied two important classes of algorithms requiring +or-2/sup b/ communications: +or-2/sup b/-descend, and +or-2/sup b/-ascend. Let N=2/sup n/ be the number of PEs in a SIMD hypercube which restricts all communications to a single fixed dimension at a time. He has developed an efficient O(n) algorithm for the descend class, and also obtained a simple O(n/sup 2//logn) algorithm for the ascend class, requiring O(logn) words of local memory per PE. In the present paper he presents two new algorithms for the ascend class on a SIMD hypercube. The first algorithm runs in O(n/sup 1.5/) time and requires O(1) space per PE. The second algorithm, which is discussed only briefly, runs in O(n square root n/log n) time and requires O(logn) space per PE.