Abstract. This paper defines the properties of FDT (Flow Dependence Tail set) and FDH (Flow Dependence Head set), and presents two partitioning methods for finding two parallel regions in two-dimensional solution space. One is the region partitioning method by intersection of FDT and FDH. Another is the region partitioning method by two given equations. Both methods show how to determine whether the intersection of FDT and FDH is empty or not. In the case that FDT does not overlap FDH, we will divide the iteration space into two parallel regions by a line. The iterations within each area can be fully executed in parallel. So, we can find two parallel regions for doubly nested loops with non-uniform dependences for maximizing parallelism.

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