Polytope Extensions with Linear Diameters
Combinatorics
2024-09-25 v3
Abstract
We describe constructions of extended formulations that establish a certain relaxed version of the Hirsch conjecture and prove that if there is a pivot rule for the simplex algorithm for which one can bound the number of steps by a polynomial in the diameter plus the number of facets of the polyhedron of feasible solutions then the general linear programming problem can be solved in strongly polynomial time.
Cite
@article{arxiv.2307.05246,
title = {Polytope Extensions with Linear Diameters},
author = {Volker Kaibel and Kirill Kukharenko},
journal= {arXiv preprint arXiv:2307.05246},
year = {2024}
}
Comments
24 pages, 4 figures