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We consider a strongly NP-hard problem of finding a family of dis-joint subsets with given cardinalities in a finite set of points from Euclidean space. The minimum of the sum over all subsets from required family of the sum of the squared distances from the elements of these subsets to their centers is used as a search criterion. The subsets centers are… (More)

We consider a strongly NP-hard Euclidean problem of finding a sub-sequence in a finite sequence under the criterion of the minimum sum of squared distances from the elements of sought subsequence to its geometric center (cen-troid). It is assumed that the sought subsequence contains a given number of elements. In addition, sought subsequence has to satisfy… (More)

We analyze the complexity status of one of the known discrete optimization problems where the optimization criterium is switched from max to min. In the considered problem, we search in a finite set of Euclidean vectors (points) a subset that minimizes the squared norm of the sum of its elements divided by the cardinality of the subset. It is proved that if… (More)

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