Perfect Latin squares and parallel array access

Abstract

A new nonlinear skewing scheme is proposed for parallel array access. We introduce a new Latin square(perfect Latin square) which has several properties useful for parallel array access. A sufficient condition for the existence of perfect Latin squares and a simple construction method for perfect Latin squares are presented. The resulting skewing scheme provides conflict free access to various subsets of an N x N array using N memory modules. When the number of memory modules is an even power of two, address generation is performed in constant time using a simple circuit. This scheme is the first memory scheme that achieves constant time access to rows, columns, diagonals, and N 1/2 x N 1/2 subarrays of an N x N array using the minimum number of memory modules.