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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)

- Alexandr Galashov, Alexander Kelmanov
- DOOR
- 2016

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

- A M KELMANOV
- Aptechnoe delo
- 1964

In this paper, we consider the problem of finding a maximum cardinality subset of vectors, given a constraint on the normalized squared length of vectors sum. This problem is closely related to Problem 1 from (Eremeev, Kel’manov, Pyatkin, 2016). The main difference consists in swapping the constraint with the optimization criterion. We prove that the… (More)

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