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Latin Squares for Parallel Array Access
April 1993 (vol. 4 no. 4)
pp. 361-370

A parallel memory system for efficient parallel array access using perfect latin squares asskewing functions is discussed. Simple construction methods for building perfect latinsquares are presented. The resulting skewing scheme provides conflict free access toseveral important subsets of an array. The address generation can be performed inconstant time with simple circuitry. The skewing scheme can provide constant timeaccess to rows, columns, diagonals, and N/sup 1/2/*N/sup 1/2/ subarrays of an N*Narray with maximum memory utilization. Self-routing Benes networks can be used torealize the permutations needed between the processing elements and the memorymodules. Two skewing schemes that provide conflict free access to three-dimensionalarrays are also discussed. Combined with self-routing Benes networks, these schemesprovide efficient access to frequently used subsets of three-dimensional arrays.

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Index Terms:
Index Termsparallel array access; parallel memory system; perfect latin squares; skewing functions;conflict free access; skewing scheme; self-routing Benes networks; multiprocessorinterconnection networks; shared memory systems; storage management
K. Kim, V.K. Prasanna, "Latin Squares for Parallel Array Access," IEEE Transactions on Parallel and Distributed Systems, vol. 4, no. 4, pp. 361-370, April 1993, doi:10.1109/71.219753
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