An Efficient Algorithm for the Optimal Linear Schedule of Uniform Dependence Algorithms

To whom all correspondence should be addressed Abstract Real-time dynamic control of robot manipulators incurs significant computational load, that can be tackled by parallel processing techniques. One of the most promising areas of research in this field is the area of automatic parallelization of sequential algorithms. In this paper we present an efficient algorithm for the parallelization of nested FOR(DO)-loops with uniform data dependencies. Our work is based on the hyperplane concept, i.e. a set of computations which can be executed simultaneously and which lie on a group of parallel hyperplanes. The resulting hyperplane is guaranteed to be optimal. The primary task when dealing with serial algorithms which will be executed in parallel architectures, is finding a time mapping that defines a new execution ordering and enables parallelism. Our objective is to schedule computations in time, for a specific class of algorithms, the uniform dependence algorithms. The method presented here finds the optimal linear mapping, and outperforms all the previously presented methods in terms of time complexity.