Using Basis Dependence Distance Vectors to Calculate the Transitive Closure of Dependence Relations by Means of the Floyd-Warshall Algorithm

In this paper, we present a modified Floyd-Warshall algorithm, where the most time-consuming part – calculating transitive closure describing self-dependences for each loop statement – is computed by means of basis dependence distance vectors derived from all vectors describing self-dependences. We demonstrate that the presented approach reduces the transitive closure calculation time for parameterized graphs representing all dependences in the loop in comparison with techniques implemented in the Omega and ISL libraries. This increases the applicability scope of techniques based on transitive closure of dependence graphs. Experimental results for NASA Parallel Benchmarks are discussed.

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