Transitive Closure of a Union of Dependence Relations for Parameterized Perfectly-Nested Loops

This paper presents a new approach for computing the transitive closure of a union of relations describing all the dependences in both uniform and quasi-uniform perfectly-nested parameterized loops. This approach is based on calculating the basis of a dependence distance vectors set. The procedure has polynomial time complexity for most steps of calculations. This allows us to effectively extract both fineand coarse-grained parallelism in loops using techniques based on applying the transitive closure of dependence relations. The effectiveness and time complexity of the approach are evaluated for loops provided by the NAS Parallel Benchmark Suite.