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Maximum Diversity Problem with Squared Euclidean Distance

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Book cover Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

Abstract

In this paper we consider the following Maximum Diversity Subset problem. Given a set of points in Euclidean space, find a subset of size M maximizing the squared Euclidean distances between the chosen points. We propose an exact dynamic programming algorithm for the case of integer input data. If the dimension of the Euclidean space is bounded by a constant, the algorithm has a pseudo-polynomial time complexity. Using this algorithm, we develop an FPTAS for the special case where the dimension of the Euclidean space is bounded by a constant. We also propose a new proof of strong NP-hardness of the problem in the general case.

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Acknowledgements

The study presented in Sect. 4 was supported by the Russian Foundation for Basic Research project 19-01-00308. The study presented in Sect. 6 was supported by the Russian Academy of Science (the Program of basic research), projects 0314-2019-0015, 0314-2019-0019, and in Sect. 3 by the Russian Ministry of Science and Education under the 5-100 Excellence Programme.

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Anton V. Eremeev, Alexander V. Kel’manov & Artem V. Pyatkin

  2. Dostoevsky Omsk State University, Omsk, Russia

    Anton V. Eremeev

  3. Novosibirsk State University, Novosibirsk, Russia

    Alexander V. Kel’manov & Artem V. Pyatkin

  4. United Institute of Informatics Problems, Minsk, Belarus

    Mikhail Y. Kovalyov

Authors
  1. Anton V. Eremeev
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  2. Alexander V. Kel’manov
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  3. Mikhail Y. Kovalyov
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  4. Artem V. Pyatkin
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Corresponding author

Correspondence to Anton V. Eremeev .

Editor information

Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Eremeev, A.V., Kel’manov, A.V., Kovalyov, M.Y., Pyatkin, A.V. (2019). Maximum Diversity Problem with Squared Euclidean Distance. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_38

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22628-2

  • Online ISBN: 978-3-030-22629-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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