Locating a semi-obnoxious covering facility with repelling polygonal regions

Locating a Semi-Obnoxious Facility with Repelling Polygonal Regions

In this work, a semi-obnoxious facility must be located in the Euclidean plane to give service to a group of customers. Simultaneously, a set of populated areas, with shapes approximated via polygons, must be protected from the negative effects derived from that facility. The problem is formulated as a margin maximization model, following a strategy successfully used in Support Vector Machines....

Locating a Semi-Obnoxious Facility on a Network with the Elliptic Maximin and Network Minisum Objectives

Covering Simple Polygonal Regions by Ellipses

We study the problem of how to cover simple polygonal rectilinear regions by a small set of axis–parallel ellipses. This question is well motivated by a special pattern recognition task where one has to identify ellipse shaped protein spots in 2–dimensional electrophoresis images. We present and discuss various algorithmic approaches towards this problem ranging from a brute force method, to a ...

Computing obnoxious 1-corner polygonal chains

We consider an obnoxious facility location problem in which the facility is a trajectory consisting of a bounded length polygonal chain of two edges having extremes anchored at two given points. In other words, given a set S of points in the plane and a positive value l0, we want to compute an anchored 1-corner polygonal chain having length at most l0 such that the minimum distance to the point...

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 ...