Diameter of Polyhedra: Limits of Abstraction

Authors:
Friedrich Eisenbrand;Nicolai Hähnle;Alexander Razborov;Thomas Rothvoß
Affiliations:
Institute of Mathematics, EPFL, CH-1015 Lausanne, Switzerland;Institute of Mathematics, EPFL, CH-1015 Lausanne, Switzerland;University of Chicago, Chicago, Illinois 60637;Institute of Mathematics, EPFL, CH-1015 Lausanne, Switzerland
Venue:
Mathematics of Operations Research
Year:
2010

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Abstract

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.