Pipelined Parallel Prefix Computations, and Sorting on a Pipelined Hypercube

• Published in: Journal of parallel and distributed computing Vol. 17; no. 4; pp. 374 - 380
• Main Authors: Mayr, Ernst W., Plaxton, C.Greg
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 1993; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Exact sciences and technology; Software; Parallelism; Binary tree; Pipeline processeur; Hypercube; Sorting
• ISSN: 0743-7315; 1096-0848
• DOI: 10.1006/jpdc.1993.1037

This paper brings together a number of previously known techniques in order to obtain practical and efficient "pipelined" implementations of the prefix operation for the complete binary tree, hypercube, and shuffle-exchange families of networks. In each case, we provide a scheme for performing k prefix operations in O( k + lg p) time on p processors. The same bounds are shown to apply to the "data distribution" operation of Ullman ( Computational Aspects of VLSI, Computer Science Press, Rockville, MD, 1984). The data distribution primitive leads to a simplified implementation of the optimal merging algorithm of Varman and Doshi (Tech. Rep. TR-8802, Rice University, Department of Electrical and Computer Engineering, Feb. 1988), which runs on a pipelined model of the hypercube. Finally, a pipelined version of the multi-way merge sort of Nassimi and Sahni ( JACM 29 (1982), 642-667), running on the pipelined hypercube model, is described. Given p processors and n < p lg p values to be sorted, the running time of the pipelined algorithm is O(lg 2 p/lg(( p lg p)/ n)).