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Aequationes mathematicae

, Volume 91, Issue 2, pp 331–352 | Cite as

On the covering radius of lattice zonotopes and its relation to view-obstructions and the lonely runner conjecture

  • Matthias Henze
  • Romanos-Diogenes Malikiosis
Article
  • 80 Downloads

Abstract

The goal of this paper is twofold; first, we show the equivalence between certain problems in geometry, such as view-obstructions, billiard ball motions, and the estimation of covering radii of lattice zonotopes. Second, we utilize the latter interpretation and provide upper bounds of said radii by virtue of the Flatness Theorem. Our results allow us to specify how rational dependencies in the view-direction influence the obstruction parameter. These problems are similar in nature to the famous Lonely Runner Problem for which we draw analogous conclusions.

Keywords

Covering radius zonotope view-obstruction Lonely Runner Conjecture billiard ball motion Flatness theorem 

Mathematics Subject Classification

Primary 52C17 Secondary 11H31 11J13 52C07 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany
  2. 2.Technische Universität Berlin, Institut für MathematikBerlinGermany

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