Eisenbrand, Friedrich
HĂ¤hnle, Nicolai
Razborov, Alexander
Rothvoss, Thomas
Diameter of Polyhedra: Limits of Abstraction
Mathematics of Operations Research
1526-5471
10.1287/moor.1100.0470
35
4
786-794
We investigate the diameter of a natural abstraction of the 1-skeleton of polyhedra. Even if this abstraction is more general than other abstractions previously studied in the literature, known upper bounds on the diameter of polyhedra continue to hold here. On the other hand, we show that this abstraction has its limits by providing an almost quadratic lower bound.
convex geometry;
disjoint coverings;
Hirsch conjecture;
polyhedra;
D-Step Conjecture;
Simplex Algorithm;
Polytopes;
Graphs;
Cubes;
2010
http://infoscience.epfl.ch/record/164208/files/limitsofabstraction-published.pdf;