Improved algorithms for placing undesirable facilities

We improve a number of existing algorithms for determining the location of one or more undesirable facilities amidst a set P of n demand points, under various constraints and distance functions. We assume that the demand points reside within some given bounded region R. Applying concepts and techniques from Computational Geometry, we provide e cient algorithms for the following problems: 1. Brimberg Mehrez '94: Locate k undesirable facilities within R under the constraints that the smallest distance between each demand point and the facilities is greater than a given r, and the distance between any two facilities is greater than a given d. Under the L 1 (L 1 ) norm we present e cient algorithms for any k, and under the L 2 norm we can locate e ciently two such facilities. In all cases R is assumed to be an axis-parallel rectangle. 2. Drezner Wesolowsky '94: Given a set of weighted demand points contained in an axis-parallel rectangular region (resp. circular region) R, and given a smaller axis-parallel rectangle (resp. circle) r, locate r within R such that the sum of weights of the demand points in r is minimized.