English

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.

Keywords

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

R2 v1 2026-06-28T11:27:05.914Z