Facility Location Constrained to a Polygonal Domain

Abstract

We develop efficient algorithms for locating an obnoxious facility in a simple polygonal region and for locating a desirable facility in a simple polygonal region. Many realistic facility location problems require the facilities to be constrained to lie in a simple polygonal region. Given a set S of m demand points and a simple polygon R of n vertices, we first show how to compute the location of an obnoxious facility constrained to lie in R, in O((m + n) log m + m log n) time. We then show how to compute the location of a desirable facility constrained to lie in R, also in O((m + n) log m + m log n) time. Both running times are an improvement over the known algorithms in the literature. Finally, our results generalize to the setting where the facility is constrained to lie within a set of simple polygons as opposed to a single polygon at a slight increase in complexity.