Polytope Extensions with Linear Diameters
arXiv:2307.05246
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.
24 pages, 4 figures