Copyright © 2009 Jafar Fathali et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let weighted points be given in the plane . For each point
a radius is given which is the expected ideal distance from this point
to a new facility. We want to find the location of a new facility such
that the sum of the weighted errors between the existing points and
this new facility is minimized. This is in fact a nonconvex optimization problem. We show that the optimal solution lies in an extended rectangular hull of the existing points. Based on this finding then an
efficient big square small square (BSSS) procedure is proposed.