A two-stage solution approach to multidimensional periodic scheduling

We present a two-stage solution approach to the multidimensional periodic scheduling (MPS) problem. This problem originates from the design of high-throughput digital-signal-processor systems, where highly parallel execution of loops is of utmost importance. We introduce the concept of multidimensional periodic operations in order to cope with problems originating from loop hierarchies and explicit timing requirements. In the first stage of the approach, we assign periods to the multidimensional periodic operations such that storage costs are minimized. This is done by means of branch-and-bound, based on a linear programming and constraint-generation technique. In the second stage, we assign start times to the operations and determine on which processing units (PUs) they are executed. This is done by means of an iterative approach. The two major subproblems of MPS concerning checking data dependency constraints and PU constraints are solved by means of an all-integer integer-linear-programming technique. This technique is used as a subroutine in the above two stages. The effectiveness and efficiency of the approach are good, which is illustrated by means of some practical examples.