Using basis dependence distance vectors in the modified Floyd-Warshall algorithm

In this paper, we present a modified Floyd–Warshall algorithm, where the most time-consumingpart—calculating transitive closure describing self-dependences for each loop statement—is computed applying 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 that yielded by means of techniques implemented in the Omega and ISL libraries. This increases the applicability scope of techniques based on transitive closure of dependence graphs and being aimed at building optimizing compilers. Experimental results for NASA Parallel Benchmarks are discussed.