Design of Space-Optimal Regular Arrays for Algorithms with Linear Schedules
IEEE Transactions on Computers
An introduction to processor-time-optimal systolic arrays
Highly parallel computaions
Processor Lower Bound Formulas for Array Computations and Parametric Diophantine Systems
IPPS '98 Proceedings of the 12th. International Parallel Processing Symposium on International Parallel Processing Symposium
Mapping rectangular mesh algorithms onto asymptotically space-optimal arrays
Journal of Parallel and Distributed Computing
A step towards unifying schedule and storage optimization
ACM Transactions on Programming Languages and Systems (TOPLAS)
Journal of Parallel and Distributed Computing
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The mapping of a systolic algorithm onto a regularly connected array architecture can be considered as a linear transformation problem. However, to derive the 'optimal' transformation is difficult because the necessary optimizations involve discrete decision variables and the cost functions do not usually have closed-form expressions. The paper considers the derivation of a space-optimal (minimum processor count) mapping of a given time performance. Utilizing some recent results from the geometry of numbers, it is shown that the solution space for this discrete optimization problem can be nicely bounded and hence, the optimal solution can be efficiently determined with enumeration for practical cases. Examples are provided to demonstrate the effectiveness of this approach.