@article{, author = {Brieden, Andreas; Gritzmann, Peter}, title = {On Clustering Bodies: Geometry and Polyhedral Approximation}, editor = {}, booktitle = {}, series = {}, journal = {Discrete & Computational Geometry}, address = {}, publisher = {}, edition = {}, year = {2010}, isbn = {}, volume = {44}, number = {3}, pages = {508-534}, url = {}, doi = {10.1007/s00454-009-9226-7}, keywords = {Computational convexity ; Optimization ; Geometric clustering ; Convex maximization ; Polynomial approximation ; Permutahedron}, abstract = {The present paper studies certain classes of closed convex sets in finite-dimensional real spaces that are motivated by their application to convex maximization problems, most notably, those evolving from geometric clustering. While these optimization problems are ℕℙ-hard in general, polynomial-time approximation algorithms can be devised whenever appropriate polyhedral approximations of their related clustering bodies are available. Here we give various structural results that lead to tight approximations.}, note = {}, institution = {Universität der Bundeswehr München, Fakultät für Wirtschafts- und Organisationswissenschaften, WOW 1 - Institut für Controlling, Finanz- und Risikomanagement, Professur: Brieden, Andreas}, }