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<p><it>Abstract—</it>In this paper, we present some new regular iterative algorithms for matrix multiplication and transitive closure. With these algorithms, by spacetime mapping the 2-D arrays with <math><tmath>$2N - 1$</tmath></math> and <math><tmath>$\lceil (3N - 1)/2\rceil$</tmath></math> execution times for matrix multiplication can be obtained. Meanwhile, we can derive a 2-D array with <math><tmath>$4N - 2$</tmath></math> execution time for transitive closure based on the sequential Warshall-Floyd algorithm. All these new 2-D arrays for matrix multiplication and transitive closure have the advantages of faster and more regular than other previous designs.</p><p><it>Index Terms—</it>Algorithm mapping, matrix multiplication, mesh array, systolic array, spherical array, transitive closure, VLSI architecture.</p>

P. Chang and J. Tsay, "Some New Designs of 2-D Array for Matrix Multiplication and Transitive Closure," in IEEE Transactions on Parallel & Distributed Systems, vol. 6, no. , pp. 351-362, 1995.
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