A processor-time-minimal systolic array for cubical mesh algorithms
- 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:
- National Science Foundation (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), Vol. 3:1; ISSN 1045-9219
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ARRAY PROCESSORS
DESIGN
PARALLEL PROCESSING
ALGORITHMS
DISTRIBUTED DATA PROCESSING
MESH GENERATION
TWO-DIMENSIONAL CALCULATIONS
DATA PROCESSING
MATHEMATICAL LOGIC
PROCESSING
PROGRAMMING
990200* - Mathematics & Computers