Abstract
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 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.
Highlights
Resolving many problems is based on calculating transitive closures of graphs Diestel (2010)
The goals of experiments were to evaluate the effectiveness and time complexity of the proposed approach for calculating relation Rk∗k and using it in the modified Floyd–Warshall algorithm for loops provided by the well-known NAS Parallel Benchmark (NPB) Suite from NASA and compare received results with the effectiveness and time complexity of techniques implemented in the ISL and Omega
We presented a modified Floyd–Warshall algorithm, where the most time consuming part is calculated by means of basis dependence distance vectors
Summary
Resolving many problems is based on calculating transitive closures of graphs Diestel (2010). We deal with parameterized graphs whose number of vertices is represented with an expression including structure parameters. The following concepts of linear algebra are used in the approach presented in this paper: vector, vector space, field, integral linear combination, linear independence. Definition 1 (Integer Lattice) Let {a1, a2, ..., am} be a set of linearly independent integer vectors. + λmam | λ1, ..., λm ∈ Z} is called an integer lattice generated by the basis {a1, a2, ..., am}. Definition 2 (Basis) A basis B of an integer lattice over field Z is a linearly independent subset of that generates. Every finite-dimensional vector space has a basis Shoup (2005)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
