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International Workshop on Computer Algebra in Scientific Computing

CASC 2020: Computer Algebra in Scientific Computing pp 282–306Cite as

Complexity Estimates for Fourier-Motzkin Elimination

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12291)

Abstract

In this paper, we propose an efficient method for removing all redundant inequalities generated by Fourier-Motzkin Elimination. This method is based on an improved version of Balas’ work and can also be used to remove all redundant inequalities in the input system. Moreover, our method only uses arithmetic operations on matrices and avoids resorting to linear programming techniques. Algebraic complexity estimates and experimental results show that our method outperforms alternative approaches, in particular those based on linear programming and the simplex algorithm.

Keywords

  • Polyhedral set
  • Fourier-Motzkin Elimination
  • Algebraic complexity
  • Efficient implementation

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Notes

  1. 1.

    It should be noted that, although we are using his idea, we have found a flaw in Balas’ paper. In fact, the last inequality in representation of \(W^0\) is written as equality that paper.

  2. 2.

    For example, P is generated by \(\{(1,2,3,4)^t, (2,3,4,5)^t, (2,3,7,9)^t\}\), the projection of P onto the last two coordinates is generated by \(\{(3,4)^t, (4,5)^t, (7,9)^t\}\).

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Authors and Affiliations

  1. Jiangsu University, Zhenjiang, China

    Rui-Juan Jing

  2. Western University, London, ON, Canada

    Marc Moreno-Maza & Delaram Talaashrafi

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  1. Rui-Juan Jing
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  2. Marc Moreno-Maza
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  3. Delaram Talaashrafi
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Correspondence to Delaram Talaashrafi .

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Editors and Affiliations

  1. University of Lille, Villeneuve d’Ascq, France

    Prof. François Boulier

  2. Coventry University, Coventry, UK

    Dr. Matthew England

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Prof. Timur M. Sadykov

  4. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Jing, RJ., Moreno-Maza, M., Talaashrafi, D. (2020). Complexity Estimates for Fourier-Motzkin Elimination. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2020. Lecture Notes in Computer Science(), vol 12291. Springer, Cham. https://doi.org/10.1007/978-3-030-60026-6_16

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  • DOI: https://doi.org/10.1007/978-3-030-60026-6_16

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