Optimal fine and medium grain parallelism detection in polyhedral reduced dependence graphs

This paper proposes an optimal algorithm for detecting fine or medium grain parallelism in nested loops whose dependences are described by an approximation of distance vectors by polyhedra. In particular it is optimal for direction vectors, which generalizes Wolf and Lam's algorithm (1991) to the case of several statements. It relies on a dependence uniformization process and an parallelization techniques related to system of uniform recurrence equations.