Automatic parallelization in the polytope model

The aim of this paper is to explain the importance of polytope and polyhedra in automatic parallelization. We show that the semantics of parallel programs is best described geometrically, as properties of sets of integral points in n-dimensional spaces, where n is related to the maximum nesting depth of DO loops. The needed properties translate nicely to properties of polyhedra, for which many algorithms have been designed for the needs of optimization and operation research. We show how these ideas apply to scheduling, placement and parallel code generation.