Clustering to minimize the sum of volumes of convex hulls of clusters is NP-complete

Terminology and Notation. Let m be 8 positive integer, R m the m-dimensional Euclidean space and Z m the set of all integer-lattice points in R m . For e finite nonempty subset S of R m let CH(S) denote the convex hull of S , and ~(S) the usual geometrical volume of CH(S) . Symbol ~(., .) will denote the Euclidean distance in R 2 • Our NP-completeness terminology (in particular concerning graphs and multigraphs) is standard, see e.g. [2~ • The symbol Kp +) , where p is a given positive integer, denotes a circuit (in an undirected graph or multigraph) of length p .