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.
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Brieden, A., Gritzmann, P. On Clustering Bodies: Geometry and Polyhedral Approximation. Discrete Comput Geom 44, 508–534 (2010). https://doi.org/10.1007/s00454-009-9226-7
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DOI: https://doi.org/10.1007/s00454-009-9226-7