Issue No. 02 - February (1995 vol. 6)

ISSN: 1045-9219

pp: 196-199

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.342133

ABSTRACT

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

INDEX TERMS

CITATION

Kuo-Liang Chung, "Prefix Computations on a Generalized Mesh-Connected Computer with Multiple Buses",

*IEEE Transactions on Parallel & Distributed Systems*, vol. 6, no. , pp. 196-199, February 1995, doi:10.1109/71.342133