IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v74y2019i4d10.1007_s10898-018-00733-2.html
   My bibliography  Save this article

Local search approximation algorithms for the sum of squares facility location problems

Author

Listed:
  • Dongmei Zhang

    (Shandong Jianzhu University)

  • Dachuan Xu

    (Beijing University of Technology)

  • Yishui Wang

    (Chinese Academy of Sciences)

  • Peng Zhang

    (Shandong University)

  • Zhenning Zhang

    (Beijing University of Technology)

Abstract

In this paper, we study the sum of squares facility location problem (SOS-FLP) which is an important variant of k-means clustering. In the SOS-FLP, we are given a client set $$ \mathcal {C} \subset \mathbb {R}^p$$ C ⊂ R p and a uniform center opening cost $$f>0$$ f > 0 . The goal is to open a finite center subset $$F \subset \mathbb {R}^p$$ F ⊂ R p and to connect each client to the closest open center such that the total cost including center opening cost and the sum of squares of distances is minimized. The SOS-FLP is introduced firstly by Bandyapadhyay and Varadarajan (in: Proceedings of SoCG 2016, Article No. 14, pp 14:1–14:15, 2016) which present a PTAS for the fixed dimension case. Using local search and scaling techniques, we offer the first constant approximation algorithm for the SOS-FLP with general dimension. We further consider the discrete version of SOS-FLP, in which we are given a finite candidate center set with nonuniform opening cost comparing with the aforementioned (continue) SOS-FLP. By exploring the structures of local and optimal solutions, we claim that the approximation ratios are $$7.7721+ \epsilon $$ 7.7721 + ϵ and $$9+ \epsilon $$ 9 + ϵ for the continue and discrete SOS-FLP respectively.

Suggested Citation

  • Dongmei Zhang & Dachuan Xu & Yishui Wang & Peng Zhang & Zhenning Zhang, 2019. "Local search approximation algorithms for the sum of squares facility location problems," Journal of Global Optimization, Springer, vol. 74(4), pages 909-932, August.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:4:d:10.1007_s10898-018-00733-2
    DOI: 10.1007/s10898-018-00733-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-018-00733-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-018-00733-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sai Ji & Gaidi Li & Dongmei Zhang & Xianzhao Zhang, 2023. "Approximation algorithms for the capacitated correlation clustering problem with penalties," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-16, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:74:y:2019:i:4:d:10.1007_s10898-018-00733-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.