On the complexity of some problems of searching for a family of disjoint clusters
- Authors: Kel'manov A.V.1,2, Pyatkin A.V.1,2, Khandeev V.I.1,2
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
- Novosibirsk State University
- Issue: Vol 484, No 4 (2019)
- Pages: 387-392
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/12540
- DOI: https://doi.org/10.31857/S0869-56524844387-392
- ID: 12540
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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.
About the authors
A. V. Kel'manov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences; Novosibirsk State University
Author for correspondence.
Email: kelm@math.nsc.ru
Russian Federation, 4, Acad. Koptyug prospect, Novosibirsk, 630090; 1, Pirogova street, Novosibirsk, 630090
A. V. Pyatkin
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences; Novosibirsk State University
Email: artem@math.nsc.ru
Russian Federation, 4, Acad. Koptyug prospect, Novosibirsk, 630090; 1, Pirogova street, Novosibirsk, 630090
V. I. Khandeev
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences; Novosibirsk State University
Email: khandeev@math.nsc.ru
Russian Federation, 4, Acad. Koptyug prospect, Novosibirsk, 630090; 1, Pirogova street, Novosibirsk, 630090
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