The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S ⊆ V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered.

Introduction Imagine, for a second, a doorman who behaves as automatic doors do. He does not acknowledge you when you approach or pass by. He gives no hint which door can or will open—until you wander within six feet of the door, whereupon he flings the door wide open. If you arrived after hours, you might stand in front of the doors for awhile before you realize that the doors are locked, beca...

We present e cient algorithms for several instances of the following facility location problem. (Facilities and demand sites are represented as points in the plane.) Place k obnoxious facilities, with respect to n given demand sites and m given regions, where the goal is to maximize the minimal distance between a demand site and a facility, under the constraint that each of the regions must con...

In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various existing facility points; 2) Maximize the minimum distance from the facility to be located to the existing facility points; 3) Maximize the number of existing facility points covered. Area re...

The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP-hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been rec...

In this paper we study the following general MaxMinoptimization problem concerning undesirable (obnoxious) facility location: Given a set of n sites S inside a convex region P , construct m garbage deposit sites Vm such that the minimum distance between these sites Vm and the union of S and Vm, Vm∪S, is maximized. We present a general method using Voronoi diagrams to approximately solve two suc...