Extensions: Locating Other Objects

Abstract

With the exception of Section 6.4, where we discussed the location of a line segment as an example for a restricted line location problem, we dealt with the location of lines and hyperplanes so far. A lot of extensions to these affine structures are possible: In the plane one might locate other one-dimensional facilities, e.g., line segments, paths, trees, circles, etc. The location of two-dimensional facilities such as rectangles, squares, or balls seems to be an interesting subject, too. But in the literature very little is known about the location of other objects New, when the distance between New and a point x is defined as the distance between x and its closest point in New, i.e.