Department of Mathematics and Statistics at the Faculty of Science
University of Calgary
On the average distance from the Fermat-Weber center of a planar convex body
Submitted by ppaterso on Wed, 02/25/2009 - 11:54am.
Feb 27 2009 - 4:00pm
Feb 27 2009 - 5:00pm
Speaker:
Csaba D. Toth (Dept. of Math. and Stats., U of C)
Location:
MS 431Discrete Geometry Seminar
The Fermat-Weber center (FW center) of a planar body Q is the
point in the plane
from which the average distance to the points in Q is minimal. This talk presents new
bounds on the average distance from the FW center of convex body Q to the points
of Q in terms of the diameter of Q. We prove a conjecture by Carmi, Har-Peled and
Katz, and show that the diameter of any convex body is less than 6 times the average
distance from its FW center. From the other direction, we show that the diameter of
any convex body is more than 2.866 times the average distance from its FW center.
The minimum value of their ratio is conjectured to be 3, which is attained for disks.
(Joint work with A. Dumitrescu.)
from which the average distance to the points in Q is minimal. This talk presents new
bounds on the average distance from the FW center of convex body Q to the points
of Q in terms of the diameter of Q. We prove a conjecture by Carmi, Har-Peled and
Katz, and show that the diameter of any convex body is less than 6 times the average
distance from its FW center. From the other direction, we show that the diameter of
any convex body is more than 2.866 times the average distance from its FW center.
The minimum value of their ratio is conjectured to be 3, which is attained for disks.
(Joint work with A. Dumitrescu.)