IDEAS home Printed from https://ideas.repec.org/a/spr/jcomop/v25y2013i2d10.1007_s10878-012-9452-4.html
   My bibliography  Save this article

Some variations on constrained minimum enclosing circle problem

Author

Listed:
  • Arindam Karmakar

    (Tezpur University)

  • Sandip Das

    (ACM Unit)

  • Subhas C. Nandy

    (ACM Unit)

  • Binay K. Bhattacharya

    (Simon Fraser University)

Abstract

Given a set P of n points and a straight line L, we study three important variations of minimum enclosing circle problem as follows: (i) Computing k identical circles of minimum radius with centers on L, whose union covers all the points in P. (ii) Computing the minimum radius circle centered on L that can enclose at least k points of P. (iii) If each point in P is associated with one of the k given colors, then compute a minimum radius circle with center on L such that at least one point of each color lies inside it. We propose three algorithms for Problem (i). The first one runs in O(nklogn) time and O(n) space. The second one is efficient where k≪n; it runs in O(nlogn+nk+k 2log3 n) time and O(nlogn) space. The third one is based on parametric search and it runs in O(nlogn+klog4 n) time. For Problem (ii), the time and space complexities of the proposed algorithm are O(nk) and O(n) respectively. For Problem (iii), our proposed algorithm runs in O(nlogn) time and O(n) space.

Suggested Citation

  • Arindam Karmakar & Sandip Das & Subhas C. Nandy & Binay K. Bhattacharya, 2013. "Some variations on constrained minimum enclosing circle problem," Journal of Combinatorial Optimization, Springer, vol. 25(2), pages 176-190, February.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:2:d:10.1007_s10878-012-9452-4
    DOI: 10.1007/s10878-012-9452-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10878-012-9452-4
    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/s10878-012-9452-4?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.

    References listed on IDEAS

    as
    1. Dorit S. Hochbaum & David B. Shmoys, 1985. "A Best Possible Heuristic for the k -Center Problem," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 180-184, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Yi Xu & Jigen Peng & Wencheng Wang & Binhai Zhu, 2018. "The connected disk covering problem," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 538-554, February.
    2. Nicolas Dupin & Frank Nielsen & El-Ghazali Talbi, 2021. "Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front," Mathematics, MDPI, vol. 9(4), pages 1-30, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Barbara Anthony & Vineet Goyal & Anupam Gupta & Viswanath Nagarajan, 2010. "A Plant Location Guide for the Unsure: Approximation Algorithms for Min-Max Location Problems," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 79-101, February.
    2. Sergio Cabello, 2023. "Faster distance-based representative skyline and k-center along pareto front in the plane," Journal of Global Optimization, Springer, vol. 86(2), pages 441-466, June.
    3. Abdul Suleman, 2017. "On ill-conceived initialization in archetypal analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 785-808, December.
    4. Randeep Bhatia & Sudipto Guha & Samir Khuller & Yoram J. Sussmann, 1998. "Facility Location with Dynamic Distance Functions," Journal of Combinatorial Optimization, Springer, vol. 2(3), pages 199-217, September.
    5. Viswanath Nagarajan & Baruch Schieber & Hadas Shachnai, 2020. "The Euclidean k -Supplier Problem," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 1-14, February.
    6. Kobbi Nissim & Rann Smorodinsky & Moshe Tennenholtz, 2018. "Segmentation, Incentives, and Privacy," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1252-1268, November.
    7. Nicolas Dupin & Frank Nielsen & El-Ghazali Talbi, 2021. "Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front," Mathematics, MDPI, vol. 9(4), pages 1-30, February.
    8. Dongyue Liang & Liquan Mei & James Willson & Wei Wang, 2016. "A simple greedy approximation algorithm for the minimum connected $$k$$ k -Center problem," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1417-1429, May.
    9. Ye, Mao & Zhang, Peng & Nie, Lizhen, 2018. "Clustering sparse binary data with hierarchical Bayesian Bernoulli mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 32-49.
    10. Felix Bock, 2022. "Hierarchy cost of hierarchical clusterings," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 617-634, August.
    11. Xuqing Bai & Hong Chang & Xueliang Li, 2020. "More on limited packings in graphs," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 412-430, August.
    12. Gan, Jinxiang & Zhang, Guochuan & Zhang, Yuhao, 2024. "Bike rebalancing: How to find a balanced matching in the k center problem?," European Journal of Operational Research, Elsevier, vol. 316(3), pages 845-855.
    13. Sourour Elloumi & Martine Labbé & Yves Pochet, 2004. "A New Formulation and Resolution Method for the p-Center Problem," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 84-94, February.
    14. Zhuqi Miao & Balabhaskar Balasundaram & Eduardo L. Pasiliao, 2014. "An exact algorithm for the maximum probabilistic clique problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 105-120, July.
    15. Renbo Huang & Guirong Zhuo & Lu Xiong & Shouyi Lu & Wei Tian, 2023. "A Review of Deep Learning-Based Vehicle Motion Prediction for Autonomous Driving," Sustainability, MDPI, vol. 15(20), pages 1-43, October.
    16. Wei Ding & Ke Qiu, 2020. "Approximating the asymmetric p-center problem in parameterized complete digraphs," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 21-35, July.
    17. Yi Xu & Jigen Peng & Wencheng Wang & Binhai Zhu, 2018. "The connected disk covering problem," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 538-554, February.
    18. Gruia Călinescu & Xiaolang Wang, 2019. "Client assignment problems for latency minimization," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 889-900, April.
    19. Xuqing Bai & Hong Chang & Xueliang Li, 0. "More on limited packings in graphs," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-19.
    20. Raphael Kramer & Manuel Iori & Thibaut Vidal, 2020. "Mathematical Models and Search Algorithms for the Capacitated p -Center Problem," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 444-460, April.

    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:25:y:2013:i:2:d:10.1007_s10878-012-9452-4. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.