Abstract
We consider some consimilar problems of searching for disjoint subsets (clusters) in the nite set of points in Euclidean space. In these problems, it is required to maximize the minimum subset size such that the value of each intracluster quadratic variation would not exceed a given fraction (constant) of the total quadratic variation of the points of the input set with respect to its centroid. In the paper, we have proved that all the problems are NP-hard even on a line.
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