Structured scheduling of recurrence equations: Theory and practice

Abstract

We present new methods for scheduling structured systems of recurrence equations. We introduce the notion of structured dependence graph and structured scheduling. We show that the scheduling of recurrence equations leads to integer linear programs whose practical complexity is O(n3), where n is the number of constraints. We give new algorithms for computing linear and multi-dimensional structured scheduling, using existing techniques for scheduling non-structured systems of affine recurrence equations. We show that structured scheduling is more than one order of magnitude more efficient than the scheduling of corresponding inlined systems.