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

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

Computational Geometry 2018-06-15 v2

Authors: Yael Yankelevsky , Alfred M. Bruckstein

View on arXiv ↗ PDF ↗ DOI ↗

Abstract

Given N points in the plane $P_1 P_2...P_N$ and a location $\Omega$ , the union of discs with diameters $[\Omega P_i], i = 1, 2,...N$ covers the convex hull of the points. The location $\Omega_s$ 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.

Keywords

optimal disc covers Steiner center convex hull Euclidean space geometric optimization area minimization

Cite

@article{arxiv.1312.0233,
  title  = {On Optimal Disc Covers and a New Characterization of the Steiner Center},
  author = {Yael Yankelevsky and Alfred M. Bruckstein},
  journal= {arXiv preprint arXiv:1312.0233},
  year   = {2018}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

Related papers