Scheduling affine parameterized recurrences by means of variable dependent timing functions

We present new scheduling techniques for systems of affine recurrence equations. We show that it is possible to extend earlier results on affine scheduling to the case when each variable of the system is scheduled independently of the others by an affine timing-function. This new technique makes it possible to analyze systems of recurrence equations with variables in different index spaces, and multi-step systolic algorithms. We illustrate our method on dynamic programming and LU decomposition