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<p> The method of decomposing a dependence graph into multiple phases with an appropriate m-phase schedule function is useful for designing faster regular arrays for matrix multiplication and transitive closure. In this paper, we further apply this method to design several parallel algorithms for the algebraic path problem and derive N/spl times/N 2D regular arrays with execution times [9N/2]-2 (for the cylindrical array and the orthogonal one) and 4N-2 (for the spherical one).</p>
parallel algorithms; computational complexity; systolic arrays; graph theory; matrix algebra; efficient regular arrays; algebraic path problem; dependence graph decomposition; multiple phases; m-phase schedule function; matrix multiplication; transitive closure; parallel algorithms; execution times; cylindrical array; orthogonal array; spherical array; systolic array; VLSI architecture.

J. Tsay and P. Chang, "A Family of Efficient Regular Arrays for Algebraic Path Problem," in IEEE Transactions on Computers, vol. 43, no. , pp. 769-777, 1994.
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