Email this article 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, Russian Academy of Sciences
- Novosibirsk State University
- Issue: Vol 99, No 1 (2019)
- Pages: 52-56
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225620
- DOI: https://doi.org/10.1134/S1064562419010162
- ID: 225620
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Abstract
Two consimilar problems of searching for a family of disjoint subsets (clusters) in a finite set of points of Euclidean space are considered. In these problems, the task is to maximize the minimum cluster size so that the value of each intercluster quadratic variation does not exceed a given fraction (constant) of the total quadratic variation of the points of the input set with respect to its centroid. Both problems are proved to be NP-hard even on a line.
About the authors
A. V. Kel’manov
Sobolev Institute of Mathematics, Siberian Branch,Russian Academy of Sciences; Novosibirsk State University
Author for correspondence.
Email: kelm@math.nsc.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
A. V. Pyatkin
Sobolev Institute of Mathematics, Siberian Branch,Russian Academy of Sciences; Novosibirsk State University
Author for correspondence.
Email: artem@math.nsc.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
V. I. Khandeev
Sobolev Institute of Mathematics, Siberian Branch,Russian Academy of Sciences; Novosibirsk State University
Author for correspondence.
Email: khandeev@math.nsc.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
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