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arXiv · 1508.00778

Packing and covering with balls on Busemann surfaces

Victor Chepoi·Bertrand Estellon·Guyslain Naves
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Abstract

In this note we prove that for any compact subset $S$ of a Busemann surface $({\mathcal S},d)$ (in particular, for any simple polygon with geodesic metric) and any positive number $δ$, the minimum number of closed balls of radius $δ$ with centers at $\mathcal S$ and covering the set $S$ is at most 19 times the maximum number of disjoint closed balls of radius $δ$ centered at points of $S$: $ν(S) \le ρ(S) \le 19ν(S)$, where $ρ(S)$ and $ν(S)$ are the covering and the packing numbers of $S$ by $δ$-balls.

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Victor Chepoi, Bertrand Estellon, Guyslain Naves. 2017-03-09. Packing and covering with balls on Busemann surfaces. https://doi.org/10.1007/s00454-017-9872-0

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