Fast method for verifying Chernikov rules in Fourier-Motzkin elimination

  • S. I. BastrakovEmail author
  • N. Yu. Zolotykh


The problem of eliminating unknowns from a system of linear inequalities is considered. A new fast technique for verifying Chernikov rules in Fourier-Motzkin elimination is proposed, which is an adaptation of the “graph” test for adjacency in the double description method. Numerical results are presented that confirm the effectiveness of this technique.


system of linear inequalities polyhedron elimination of variables Fourier-Motzkin elimination Chernikov rules 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. N. Chernikov, Linear Inequalities (Nauka, Moscow, 1968) [in Russian].Google Scholar
  2. 2.
    G. Ziegler, Lectures on Polytopes (Springer New York, 1998).Google Scholar
  3. 3.
    S. N. Chernikov, “Convolution of systems of linear inequalities,” Dokl. Akad. Nauk SSSR 131(3), 518–521 (1960).Google Scholar
  4. 4.
    S. N. Chernikov, “The convolution of finite systems of linear inequalities,” USSR Comput. Math. Math. Phys. 5(1), 1–24 (1965).CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    T. S. Motzkin, H. Raiffa, G. L. Thompson, and R. M. Thrall, “The double description method,” in Contributions to the Theory of Games, Annals of Mathematics Studies (Princeton Univ. Press, Princeton, New Jersey, 1953), Vol. 28, No. 2, pp. 51–73.Google Scholar
  6. 6.
    K. Fukuda and A. Prodon, “Double description method revisited,” Combinatorics and Computer Science (Springer-Verlag, New York, 1996), pp. 91–111.CrossRefGoogle Scholar
  7. 7.
    N. Yu. Zolotykh, “New modification of the double description method for constructing the skeleton of a polyhedral cone,” Comput. Math. Math. Phys. 51(1), 146–156 (2012).CrossRefMathSciNetGoogle Scholar
  8. 8.
    A. M. Lukatskii and D. V. Shapot, “A constructive algorithm for folding large-scale systems of linear inequalities,” Comput. Math. Math. Phys. 48(7), 1100–1112 (2008).CrossRefMathSciNetGoogle Scholar
  9. 9.
    M. M. Deza and M. Laurent, Geometry of Cuts and Metrics (Springer-Verlag, Berlin, 1997; MTsNMO, Moscow, 2001).CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Nizhni Novgorod State UniversityNizhni NovgorodRussia

Personalised recommendations