Prefix Computations on a Generalized Mesh-Connected Computer with Multiple Buses

The mesh-connected computer with multiple buses (MCCMB) is a well-known parallel organization, providing broadcast facilities in each row and each column. In this paper, we propose a 2-D 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 tridiagonal systems, etc. A klnl x k l n 2 2-GMCCMB is constructed from a IC1 n 1 x k.1 n2 mesh organization by enhancing the power of each disjoint n 1 x n2 submesh with multiple buses (sub-2-MCCMB). Given n data, a prefix computation can be performed in O(n'/'O) time on an n3/5 x I Z ~ / ~ 2-GMCCMB, where each disjoint sub-2-MCCMB is of size n l / * x n 3 / l o . This time bound is faster than the previous time bound of O ( I Z ' / * ) for the same computation on an n5/' x n3/' 2-MCCMB. Furthermore, the time bound of our parallel prefix algorithm can be further reduced to O ( n l l " ) if fewer processors are used. Our result can be extended to the d-dimensional GMCCMB, giving a time bound of O ( n ' / ( d Z d + d ) ) for any constant d ; here, we omit the constant factors. This time bound is less than the previous time bound of O ( I I ' / ( ~ ' ~ ) ) on the d-dimensional MCCMB.