IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v26y2013i2d10.1007_s10878-012-9458-y.html
   My bibliography  Save this article

On some geometric problems of color-spanning sets

Author

Listed:
  • Wenqi Ju

    (Chinese Academy of Sciences
    Graduate University of the Chinese Academy of Sciences
    Chinese Academy of Sciences)

  • Chenglin Fan

    (Chinese Academy of Sciences)

  • Jun Luo

    (Chinese Academy of Sciences)

  • Binhai Zhu

    (Montana State University)

  • Ovidiu Daescu

    (University of Texas at Dallas)

Abstract

In this paper we study several geometric problems of color-spanning sets: given n points with m colors in the plane, selecting m points with m distinct colors such that some geometric properties of the m selected points are minimized or maximized. The geometric properties studied in this paper are the maximum diameter, the largest closest pair, the planar smallest minimum spanning tree, the planar largest minimum spanning tree and the planar smallest perimeter convex hull. We propose an O(n 1+ε ) time algorithm for the maximum diameter color-spanning set problem where ε could be an arbitrarily small positive constant. Then, we present hardness proofs for the other problems and propose two efficient constant factor approximation algorithms for the planar smallest perimeter color-spanning convex hull problem.

Suggested Citation

  • Wenqi Ju & Chenglin Fan & Jun Luo & Binhai Zhu & Ovidiu Daescu, 2013. "On some geometric problems of color-spanning sets," Journal of Combinatorial Optimization, Springer, vol. 26(2), pages 266-283, August.
    • Handle: RePEc:spr:jcomop:v:26:y:2013:i:2:d:10.1007_s10878-012-9458-y
    DOI: 10.1007/s10878-012-9458-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-012-9458-y
    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/s10878-012-9458-y?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. Yin Wang & Yinfeng Xu & Huili Zhang & Weitian Tong, 2023. "Online k-color spanning disk problems," Journal of Combinatorial Optimization, Springer, vol. 46(2), pages 1-14, September.

    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:jcomop:v:26:y:2013:i:2:d:10.1007_s10878-012-9458-y. 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.