Prefix computations on a generalized mesh-connected computer with multiple buses

Abstract

The mesh-connected computer with multiple buses (MC-CMB) is a well-known parallel organization, providing broadcast facilities in each row and each column. In this paper, we propose a 2D generalized MCCMB (2-GMCCMB) for the purpose of increasing the efficiency of executing some important applications of prefix computations such as solving Linear recurrences and tridiagonaI systems, etc. A k/sub 1/n/sub 1spl times/k/sub 1/n/sub 2/ 2-GMCCMB is constructed from a k/sub 1/n/sub 1spl times/k/sub 1/n/sub 2/ mesh organization by enhancing the power of each disjoint n/sub 1spl times/n/sub 2/ submesh with multiple buses (sub-2-MCCMB). Given n data, a prefix computation can be performed in O(n/sup 1/10/) time on an n/sup 3/5spl times/n/sup 2/5/ 2-GMCCMB, where each disjoint sub-2-MCCMB is of size n/sup 1/2spl times/n/sup 3/10/. This time bound is faster than the previous time bound of O(n/sup 1/8/) for the same computation on an n/sup 5/8spl times/n/sup 3/8/ 2-MCCMB. Furthermore, the time bound of our parallel prefix algorithm can be further reduced to O(n/sup 1/11/) if fewer processors are used. Our result can be extended to the d-dimensional GMCCMB, giving a time bound of O(n/sup 1/(d2(d)+d)/) for any constant d; here, we omit the constant factors. This time bound is less than the previous time bound of O(n/sup 1/(d2(d))/) on the d-dimensional MCCMB. >