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Analytics of the Multifacility Weber Problem

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Computational Science and Its Applications – ICCSA 2020 (ICCSA 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12251))

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Abstract

For the Weber problem of construction of the minimal cost planar weighted network connecting four terminals with two extra facilities, the solution by radicals is proposed. The conditions for existence of the network in the assumed topology and the explicit formulae for coordinates of the facilities are presented. It is shown that the bifacility network is less costly than the unifacility one. Extension of the results to the general Weber problem is also discussed.

Supported by RFBR according to the project No. 17-29-04288.

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Notes

  1. 1.

    In the quote we change the original notation of the points.

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Authors and Affiliations

  1. St. Petersburg State University, 7-9 Universitetskaya nab., St. Petersburg, 199034, Russia

    Alexei Yu. Uteshev & Elizaveta A. Semenova

Authors
  1. Alexei Yu. Uteshev
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  2. Elizaveta A. Semenova
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Corresponding author

Correspondence to Elizaveta A. Semenova .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Chair- Center of ICT/ICE, Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Clayton School of Information Technology, Monash University, Clayton, VIC, Australia

    David Taniar

  7. Department of Information Science, Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

  11. Department of Neurology, University of Massachusetts Medical School, Worcester, MA, USA

    Yeliz Karaca

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Uteshev, A.Y., Semenova, E.A. (2020). Analytics of the Multifacility Weber Problem. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science(), vol 12251. Springer, Cham. https://doi.org/10.1007/978-3-030-58808-3_29

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  • DOI: https://doi.org/10.1007/978-3-030-58808-3_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-58807-6

  • Online ISBN: 978-3-030-58808-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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