IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v19y2019i2d10.1007_s12351-017-0291-z.html
   My bibliography  Save this article

Computational complexity of the exterior point simplex algorithm

Author

Listed:
  • Sophia Voulgaropoulou

    (University of Macedonia)

  • Nikolaos Samaras

    (University of Macedonia)

  • Angelo Sifaleras

    (University of Macedonia)

Abstract

In this paper, we investigate the computational behavior of the exterior point simplex algorithm. Up until now, there has been a major difference observed between the theoretical worst case complexity and practical performance of simplex-type algorithms. Computational tests have been carried out on randomly generated sparse linear problems and on a small set of benchmark problems. Specifically, 6780 linear problems were randomly generated, in order to formulate a respectable amount of experiments. Our study consists of the measurement of the number of iterations that the exterior point simplex algorithm needs for the solution of the above mentioned problems and benchmark dataset. Our purpose is to formulate representative regression models for these measurements, which would play a significant role for the evaluation of an algorithm’s efficiency. For this examination, specific characteristics, such as the number of constraints and variables, the sparsity and bit length, and the condition of matrix A, of each linear problem, were taken into account. What drew our attention was that the formulated model for the randomly generated problems reveal a linear relation among these characteristics.

Suggested Citation

  • Sophia Voulgaropoulou & Nikolaos Samaras & Angelo Sifaleras, 2019. "Computational complexity of the exterior point simplex algorithm," Operational Research, Springer, vol. 19(2), pages 297-316, June.
    • Handle: RePEc:spr:operea:v:19:y:2019:i:2:d:10.1007_s12351-017-0291-z
    DOI: 10.1007/s12351-017-0291-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-017-0291-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12351-017-0291-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Karl-Heinz Borgwardt, 1982. "Some Distribution-Independent Results About the Asymptotic Order of the Average Number of Pivot Steps of the Simplex Method," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 441-462, August.
    2. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sophia Voulgaropoulou & Nikolaos Samaras & Nikolaos Ploskas, 2022. "Predicting the Execution Time of the Primal and Dual Simplex Algorithms Using Artificial Neural Networks," Mathematics, MDPI, vol. 10(7), pages 1-21, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guy Even & Alexander Zadorojniy, 2012. "Strong polynomiality of the Gass-Saaty shadow-vertex pivoting rule for controlled random walks," Annals of Operations Research, Springer, vol. 201(1), pages 159-167, December.
    2. Sinuany-Stern, Zilla, 2023. "Foundations of operations research: From linear programming to data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1069-1080.
    3. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:operea:v:19:y:2019:i:2:d:10.1007_s12351-017-0291-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.