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

• Authors: Kuo-Liang Chung
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 1995

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 $k_1n_1 \times k_1n_2$ 2-GMCCMB is constructed from a $k_1n_1\times k_1n_2$ mesh organization by enhancing the power of each disjoint $n_1\times n_2$ submesh with multiple buses (sub-2-MCCMB). Given $n$ data, a prefix computation can be performed in $O(n^{1/10})$ time on an $n^{3/5}\times n^{2/5}$ 2-GMCCMB, where each disjoint sub-2-MCCMB is of size $n^{1/2}\times n^{3/10}$. This time bound is faster than the previous time bound of $O(n^{1/8})$ for the same computation on an $n^{5/8}\times n^{3/8}$ 2-MCCMB. Furthermore, the time bound of our parallel prefix algorithm can be further reduced to $O(n^{1/11})$ if fewer processors are used. Our result can be extended to the $d$-dimensional GMCCMB, giving a time bound of $O(n^{1/(d2^d+d)})$ for any constant $d$; here, we omit the constant factors. This time bound is less than the previous time bound of $O(n^{1/(d2^d)})$ on the $d$-dimensional MCCMB.Index Terms驴Broadcasting, mesh-connected computers, mesh-connected computers with multiple buses, parallel algorithms, prefix computation, rectangular meshes.