A processor-time-minimal systolic array for transitive closure
Chris J. Scheiman, Peter R. Cappello · IEEE Transactions on Parallel and Distributed Systems · 1992
Using a directed acyclic graph (DAG) model of algorithms, the authors focus on processor-time-minimal multiprocessor schedules: time-minimal multiprocessor schedules that use as few processors as possible. The Kung, Lo, and Lewis (KLL) algorithm for computing the transitive closure of a relation over a set of n elements requires at least 5n-4 parallel steps. As originally reported. their systolic array comprises n/sup 2/ processing elements. It is shown that any time-minimal multiprocessor schedule of the KLL algorithm's dag needs at least n/sup 2//3 processing elements. Then a processor-time-minimal systolic array realizing the KLL dag is constructed. Its processing elements are organized as a cylindrically connected 2-D mesh, when n=0 mod 3. When n not=0 mod 3, the 2-D mesh is connected as a torus.>