Placing an Obnoxious Facility in Geometric Networks

In this paper we consider several different problems of placing an obnoxious facility on geometric networks. In particular, our main results show how to obtain efficient polynomial time algorithms for locating an obnoxious facility on the given network under various distance functions such as maximizing the total sum of distances or maximizing the smallest of the distances from the facility to the nodes of the network. Our algorithms are obtained by applying concepts and techniques from Computational Geometry such as range searching, constructing spanners and other optimization schemes.