article · arXiv (Cornell University) · 2013

Tropicalizing the simplex algorithm

Xavier Allamigeon, Pascal Benchimol, Stéphane Gaubert, Michael Joswig

Cited by 1Open access

Abstract

We develop a tropical analog of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in O(n(m+n)) time, where m is the number of constraints and n is the dimension.

Cite this paper

APA 7

Allamigeon, X., Benchimol, P., Gaubert, S., & Joswig, M. (2013). Tropicalizing the simplex algorithm. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1308.0454

MLA 9

Allamigeon, Xavier, et al. “Tropicalizing the simplex algorithm.” arXiv (Cornell University), 2013, https://doi.org/10.48550/arxiv.1308.0454.

Chicago

Allamigeon, Xavier, Pascal Benchimol, Stéphane Gaubert, and Michael Joswig. 2013. “Tropicalizing the simplex algorithm.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.1308.0454.

Harvard

Allamigeon, X. et al. (2013) ‘Tropicalizing the simplex algorithm’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.1308.0454.

BibTeX

@article{allamigeon2013tropicalizing,
  title = {{Tropicalizing the simplex algorithm}},
  author = {Allamigeon, Xavier and Benchimol, Pascal and Gaubert, Stéphane and Joswig, Michael},
  journal = {arXiv (Cornell University)},
  year = {2013},
  doi = {10.48550/arxiv.1308.0454}
}

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