An Analytical Comparison of the I-Test and Omega Test

  • David Niedzielski
  • Kleanthis Psarris
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1863)


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”).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Williams, H.P. (1976). Fourier-Motzkin Elimination Extension to Integer Programming Problems. Journal of Combinatorial Theory (A), 21:118–123.zbMATHCrossRefGoogle Scholar
  2. 2.
    Williams, H.P. (1983). A Characterisation of All Feasible Solutions to an Integer Program. Discrete Applied Mathematics, 5:147–155.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Wolfe, Michael (1996). High Performance Compilers for Parallel Computing, Redwood City, Ca.: Addison-Wesley Publishing Company.zbMATHGoogle Scholar
  4. 4.
    U. Banerjee (1988). Dependence Analysis for SuperComputing, Norwell, Mass.: Kluwer Academic Publishers.Google Scholar
  5. 5.
    U. Banerjee (1997). Dependence Analysis, Boston, Mass.: Kluwer Academic Publishers. p. 106zbMATHGoogle Scholar
  6. 6.
    Psarris, Kleanthis, David Klappholz, and Xiangyun Kong (1991). On the Accuracy of the Banerjee Test. Journal of Parallel and Distributed Computing, June, 12(2):152–158.Google Scholar
  7. 7.
    Kong, Xiangyun, Psarris Kleanthis, and David Klappholz (1991). The I-Test: An Improved Dependence Test for Automatic Parallelization and Vectorization. IEEE Transactions on Parallel and Distributed Systems, July, 2(3): 342–349.Google Scholar
  8. 8.
    Psarris, Kleanthis, Xiangyun Kong, and David Klappholz (1993). The Direction Vector I-Test. IEEE Transactions on Parallel and Distributed Systems, November, 4(11):1280–1290.Google Scholar
  9. 9.
    Psarris, Kleanthis, and Santosh Pande (1994). An Empirical Study of the I-Test for Exact Data Depedence. 1994 International Conference on Parallel Processing August, 1994Google Scholar
  10. 10.
    Pugh, William (1991) The Omega Test: A Fast and Practical Integer Programming Algorithm for Dependence Analysis. Supercomputing’ 91 Google Scholar
  11. 11.
    Pugh, William (1992). A Practical Algorithm for Exact Array Dependence Analysis. Communications of the ACM, August, 35(8): 102–114.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • David Niedzielski
    • 1
  • Kleanthis Psarris
    • 1
  1. 1.Division of Computer ScienceThe University of Texas at San AntonioSan Antonio

Personalised recommendations