Improved algorithms for placing undesirable facilities
We improve several 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 efficient algorithms for the following problems: Using tools from Computational Geometry we study two facility location problems that were previously studied by Brimberg and Mehrez (Location Sci. 2 (1) (1994) 11), and Drezner and Wesolowsky (Location Sci. 2 (2) (1994) 83). Geometric instances of facility location problems have attracted researchers from the Computational Geometry community, especially in the last few years. Computational Geometry (see, e.g., the textbook Computational GeometryAlgorithms and Applications, by de Berg et al., Berlin: Springer, 1997) deals with the efficient processing of spatial data and with geometric optimization, and thus techniques, algorithms, and data structures from this field can be effectively utilized for solving facility location problems of a geometric flavor.
computational geometry facility location maxmin minsum