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On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. V. Kel’manov, A. V. Pyatkin & V. I. Khandeev

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    A. V. Kel’manov, A. V. Pyatkin & V. I. Khandeev

Authors
  1. A. V. Kel’manov
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  2. A. V. Pyatkin
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  3. V. I. Khandeev
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Corresponding authors

Correspondence to A. V. Kel’manov, A. V. Pyatkin or V. I. Khandeev.

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Translated by I. Ruzanova

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Kel’manov, A.V., Pyatkin, A.V. & Khandeev, V.I. On the Complexity of Some Problems of Searching for a Family of Disjoint Clusters. Dokl. Math. 99, 52–56 (2019). https://doi.org/10.1134/S1064562419010162

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  • DOI: https://doi.org/10.1134/S1064562419010162

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