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On the Diameter of Lattice Polytopes

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Abstract

In this paper we show that the diameter of a d-dimensional lattice polytope in \([0,k]^n\) is at most \({\lfloor }{\left( k-\frac{1}{2}\right) d}{\rfloor }\). This result implies that the diameter of a d-dimensional half-integral polytope is at most \({\lfloor }{\frac{3}{2} d}{\rfloor }\). We also show that for half-integral polytopes the latter bound is tight for any d.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering & Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI, USA

    Alberto Del Pia

  2. Wisconsin Institute for Discovery, University of Wisconsin-Madison, Madison, WI, USA

    Carla Michini

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  1. Alberto Del Pia
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  2. Carla Michini
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Correspondence to Carla Michini.

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Editor in Charge: Günter M. Ziegler

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Del Pia, A., Michini, C. On the Diameter of Lattice Polytopes. Discrete Comput Geom 55, 681–687 (2016). https://doi.org/10.1007/s00454-016-9762-x

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  • DOI: https://doi.org/10.1007/s00454-016-9762-x

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