On Optimal Disc Covers and a New Characterization of the Steiner Center

Yael Yankelevsky; Alfred M. Bruckstein

doi:10.1016/j.comgeo.2015.10.006

paper

On Optimal Disc Covers and a New Characterization of the Steiner Center

arXiv:1312.0233 · doi:10.1016/j.comgeo.2015.10.006

Abstract

Given N points in the plane $P_{1} P_{2} ... P_{N}$ and a location $Ω$ , the union of discs with diameters $[Ω P_{i}], i = 1, 2, ... N$ covers the convex hull of the points. The location $Ω_{s}$ minimizing the area covered by the union of discs, is shown to be the Steiner center of the convex hull of the points. Similar results for $d$ -dimensional Euclidean space are conjectured.

arXiv comment14 pages, 11 figures; minor corrections, revised proof of theorem 2