@techreport{,
TITLE = {On the Width and Roundness of a Set of Points in the Plane},
AUTHOR = {Smid, Michiel and Janardan, Ravi},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/94-111},
NUMBER = {MPI-I-94-111},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {1994},
DATE = {1994},
ABSTRACT = {Let $S$ be a set of points in the plane. The width (resp.\ roundness) of $S$ is defined as the minimum width of any slab (resp.\ annulus) that contains all points of $S$. We give a new characterization of the width of a point set. Also, we give a {\em rigorous} proof of the fact that either the roundness of $S$ is equal to the width of $S$, or the center of the minimum-width annulus is a vertex of the closest-point Voronoi diagram of $S$, the furthest-point Voronoi diagram of $S$, or an intersection point of these two diagrams. This proof corrects the characterization of roundness used extensively in the literature.},
TYPE = {Research Report},
}