A processor-time-minimal systolic array for cubical mesh algorithms

Journal Article · Wed Jan 01 04:00:00 EST 1992 · IEEE Transactions on Parallel and Distributed Systems (Institute of Electrical and Electronics Engineers); (United States)

DOI:https://doi.org/10.1109/71.113078· OSTI ID:5361277

Cappello, P ^[1]

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1. California Univ., Santa Barbara, CA (United States). Dept. of Computer Science

Using a directed acyclic graph (dag) model of algorithms, the paper focuses on time-minimal multiprocessor schedules that use as few processors as possible. Such a processor-time-minimal scheduling of an algorithm's dag first is illustrated using a triangular shaped 2-D directed mesh (representing, for example, an algorithm for solving a triangular system of linear equations). Then, algorithms represented by an n {times} n {times} n directed mesh are investigated. This cubical directed mesh is fundamental; it represents the standard algorithm for computing matrix product as well as many other algorithms. Completion of the cubical mesh requires 3n - 2 steps. It is shown that the number of processing elements needed to achieve this time bound is at least (3n{sup 2/4}). A systolic array for the cubical directed mesh is then presented. It completes the mesh using the minimum number of steps and exactly (3n{sup 2/4}) processing elements: it is processor-time-minimal. The systolic array's topology is that of a hexagonally shaped, cylindrically- connected, 2-D directed mesh.

• Sponsoring Organization: NSF; National Science Foundation, Washington, DC (United States)
• OSTI ID: 5361277
• Journal Information: IEEE Transactions on Parallel and Distributed Systems (Institute of Electrical and Electronics Engineers); (United States), Journal Name: IEEE Transactions on Parallel and Distributed Systems (Institute of Electrical and Electronics Engineers); (United States) Vol. 3:1; ISSN ITDSE; ISSN 1045-9219
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
ARRAY PROCESSORS
DATA PROCESSING
DESIGN
DISTRIBUTED DATA PROCESSING
MATHEMATICAL LOGIC
MESH GENERATION
PARALLEL PROCESSING
PROCESSING
PROGRAMMING
TWO-DIMENSIONAL CALCULATIONS