Abstract
We consider three related problems of partitioning an N-element set of points in d-dimensional Euclidean space into two clusters balancing the value of the intracluster quadratic variance normalized by the cluster size in the first problem, the intracluster quadratic variance in the second problem, and the size-weighted intracluster variance in the third problem. The NP-completeness of all these problems is proved.
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Funding
This work was supported by the Russian Foundation for Basic Research (project nos. 19-01-00308 and 18-31-00398), by Basic Research Programs of the Russian Academy of Sciences (project nos. 0314-2019-0015 and 0314-2019-0014), and by the Top-5-100 Program of the Ministry of Education and Science of the Russian Federation.
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Translated by I. Ruzanova
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Kel’manov, A.V., Pyatkin, A.V. & Khandeev, V.I. Complexity of Some Problems of Quadratic Partitioning of a Finite Set of Points in Euclidean Space into Balanced Clusters. Comput. Math. and Math. Phys. 60, 163–170 (2020). https://doi.org/10.1134/S096554251911006X
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DOI: https://doi.org/10.1134/S096554251911006X