Mathematical Programming Formulations for the Bottleneck Hyperplane Clustering Problem

Abstract

We discuss a mixed-integer nonlinear programming formulation for the problem of covering a set of points with a given number of slabs of minimum width, known as the bottleneck variant of the hyperplane clustering problem. We derive several linear approximations, which we solve using a standard mixed-integer linear programming solver. A computational comparison of the performance of the different linearizations is provided. © Springer-Verlag Berlin Heidelberg 2008.