Designing efficient parallel algorithms on mech-connected computers with multiple broadcasting

Abstract

Semigroup and prefix computations on two-dimensional mesh-connected computers with multiple broadcasting (2-MCCMBs) are studied. Previously, only square 2-MCCMBs with N processing elements were considered for semigroup computations of N data items, and O(N/sup 1/6/) time was required. It is found that square machines are not the best form for semigroup computations, and an O(N/sup 1/8/)-time algorithm is derived on an N/sup 5/8/*N/sup 3/8/ rectangular 2-MCCMB. This time complexity can be further reduced to O(N/sup 1/9/) if fewer processing elements are used. Parallel algorithms for prefix computations with the same time complexities are derived.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>