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A Note on the Linear Transformation Method for Systolic Array Design
March 1990 (vol. 39 no. 3)
pp. 393-399

The use of the linear transformation method to systolize the Warshall algorithm for computing the transitive closure of a graph on a mesh-connected array (without wraparound connections) is discussed. The technique is extended to design linear systolic arrays. The advantage of this approach is easy verification of correctness, as well as synthesis of a family of arrays with tradeoffs between I/O bandwidth, number of processing elements, and local storage. The technique can be further refined to cope with problems that entail nonconstant dependency vectors.

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Index Terms:
linear transformation method; systolic array design; Warshall algorithm; transitive closure; graph; mesh-connected array; verification; correctness; I/O bandwidth; processing elements; local storage; cellular arrays; logic arrays; logic design; parallel algorithms.
W.-M. Lin, V.K.P. Kumar, "A Note on the Linear Transformation Method for Systolic Array Design," IEEE Transactions on Computers, vol. 39, no. 3, pp. 393-399, March 1990, doi:10.1109/12.48870
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