On the accuracy of the Banerjee test
Journal of Parallel and Distributed Computing - Special issue on shared-memory multiprocessors
The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
A practical algorithm for exact array dependence analysis
Communications of the ACM
Dependence Analysis for Supercomputing
Dependence Analysis for Supercomputing
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
The I Test: An Improved Dependence Test for Automatic Parallelization and Vectorization
IEEE Transactions on Parallel and Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
An Empirical Study of the I Test for Exact Data Dependence
ICPP '94 Proceedings of the 1994 International Conference on Parallel Processing - Volume 03
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The Omega test is an exact, (worst case) exponential time data dependence test. The I-Test is a polynomial time test, but is not always exact. In this paper we show the fundamental relationship between the two tests under conditions in which both tests are applicable. We show that Fourier-Motzkin Variable Elimination (FMVE), upon which the Omega test is based, is equivalent to the Banerjee Bounds Test when applied to single-dimensional array reference problems. Furthermore, we show the Omega Test's technique to refine Fourier-Motzkin Variable Elimination to integer solutions (dark shadow) is equivalent to the I-Test's refinement of the Banerjee Bounds Test (the interval equation). Finally, under the conditions we specify, we show the I-Test delivers an inconclusive answer if and only if the Omega test would require an exhaustive search to produce an exact answer (the so-called "Omega Test Nightmare").