Nearly logarithmic-time parallel algorithms for the class of ±2b ASCEND computations on a SIMD hypercube

Recently, the author has studied two important classes of algorithms requiring ±2^b communications: ±2^b-descend, and ±2^b-ascend. Let N=2 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(n²/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^1.5) time and requires O(1) space per PE. The second algorithm, which is discussed only briefly, runs in O(n√n/log n) time and requires O(logn) space per PE