Space-optimal linear processor allocation for systolic arrays synthesis

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