Diameter of polyhedra: limits of abstraction

Authors:
Friedrich Eisenbrand;Nicolai Hähnle;Thomas Rothvoß
Affiliations:
EPFL, Lausanne, Switzerland;EPFL, Lausanne, Switzerland;EPFL, Lausanne, Switzerland
Venue:
Proceedings of the twenty-fifth annual symposium on Computational geometry
Year:
2009

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Abstract

We investigate the diameter of a natural abstraction of the 1-skeleton of polyhedra. Although this abstraction is simpler than other abstractions that were previously studied in the literature, the best 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 a superlinear lower bound.