Finding Space-Optimal Linear Array for Uniform Dependence Algorithms with Arbitrary Convex Index Sets

The mapping of an n-dimensional uniform dependence algorithm onto a linear processor array can be considered as a linear transformation problem. However, to find a linear space-optimal transformation is difficult because the conditions for checking a correct mapping and the space cost function do not have closed-form expressions, especially when the index set J of an n-dimensional algorithm is of an arbitrary bounded convex index set. In this paper, we propose an enumeration method to find a space-optimal PE allocation vector for mapping an n-dimensional uniform dependence algorithm with an arbitrary bounded convex index set onto a linear processor array, assuming that a linear schedule is given a priori.