Tropicalizing the simplex algorithm
Combinatorics
2015-07-31 v2 Optimization and Control
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
@article{arxiv.1308.0454,
title = {Tropicalizing the simplex algorithm},
author = {Xavier Allamigeon and Pascal Benchimol and Stéphane Gaubert and Michael Joswig},
journal= {arXiv preprint arXiv:1308.0454},
year = {2015}
}
Comments
v1: 35 pages, 7 figures, 4 algorithms; v2: improved presentation, 39 pages, 9 figures, 4 algorithms