IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v79y2021i3d10.1007_s10589-021-00283-6.html
   My bibliography  Save this article

A dual simplex-type algorithm for the smallest enclosing ball of balls

Author

Listed:
  • Marta Cavaleiro

    (Rutgers University
    University Heights)

  • Farid Alizadeh

    (Rutgers University)

Abstract

We develop a dual simplex-type algorithm for computing the smallest enclosing ball of a set of balls and other closely related problems. Our algorithm employs a pivoting scheme resembling the simplex method for linear programming, in which a sequence of exact curve searches is performed until a new dual feasible solution with a strictly smaller objective function value is found. We utilize the Cholesky factorization and procedures for updating it, yielding a numerically stable implementation of the algorithm. We show that our algorithm can efficiently solve instances of dimension 5000 with 100000 points, often within minutes.

Suggested Citation

  • Marta Cavaleiro & Farid Alizadeh, 2021. "A dual simplex-type algorithm for the smallest enclosing ball of balls," Computational Optimization and Applications, Springer, vol. 79(3), pages 767-787, July.
    • Handle: RePEc:spr:coopap:v:79:y:2021:i:3:d:10.1007_s10589-021-00283-6
    DOI: 10.1007/s10589-021-00283-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-021-00283-6
    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/s10589-021-00283-6?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. Nguyen Mau Nam & Nguyen Hoang & Nguyen Thai An, 2014. "Constructions of Solutions to Generalized Sylvester and Fermat–Torricelli Problems for Euclidean Balls," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 483-509, February.
    2. Trevor Hale & Christopher Moberg, 2003. "Location Science Research: A Review," Annals of Operations Research, Springer, vol. 123(1), pages 21-35, October.
    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. P. M. Dearing & Mark E. Cawood, 2023. "The minimum covering Euclidean ball of a set of Euclidean balls in $$I\!\!R^n$$ I R n," Annals of Operations Research, Springer, vol. 322(2), pages 631-659, March.

    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. James F. Campbell & Morton E. O'Kelly, 2012. "Twenty-Five Years of Hub Location Research," Transportation Science, INFORMS, vol. 46(2), pages 153-169, May.
    2. Kenneth Carling & Mengjie Han & Johan Håkansson, 2012. "Does Euclidean distance work well when the p-median model is applied in rural areas?," Annals of Operations Research, Springer, vol. 201(1), pages 83-97, December.
    3. Cevriye Gencer & Emel Kizilkaya Aydogan & Coskun Celik, 2008. "A decision support system for locating VHF/UHF radio jammer systems on the terrain," Information Systems Frontiers, Springer, vol. 10(1), pages 111-124, March.
    4. Valentina Ferretti & Silvia Pomarico, 2012. "Integrated sustainability assessments: a spatial multicriteria evaluation for siting a waste incinerator plant in the Province of Torino (Italy)," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 14(5), pages 843-867, October.
    5. Liu, Haoxiang & Wang, David Z.W., 2017. "Locating multiple types of charging facilities for battery electric vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 103(C), pages 30-55.
    6. Youcef MECHOUAR & V Hovelaque & C Gaigné, 2021. "Effect of raw material substitution on the facility location decision under a carbon tax policy," Post-Print hal-04155066, HAL.
    7. Francesco Ciari & Claude Weis & Milos Balac, 2016. "Evaluating the influence of carsharing stations’ location on potential membership: a Swiss case study," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 345-369, August.
    8. Mark Horner & Michael Widener, 2011. "The effects of transportation network failure on people’s accessibility to hurricane disaster relief goods: a modeling approach and application to a Florida case study," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 59(3), pages 1619-1634, December.
    9. Sorin-Mihai Grad & Oleg Wilfer, 2019. "A proximal method for solving nonlinear minmax location problems with perturbed minimal time functions via conjugate duality," Journal of Global Optimization, Springer, vol. 74(1), pages 121-160, May.
    10. Chao-Hsien Yeh & Yi-Ru Chen, 2020. "Location model analysis of flood relief facilities: a case study of the Fazih River floodplain, Taiwan," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 103(1), pages 317-327, August.
    11. Carling, Kenneth & Han, Mengjie & Håkansson, Johan & Rebreyend, Pascal, 2012. "Distance measure and the p-median problem in rural areas," HUI Working Papers 78, HUI Research.
    12. Ashu Kedia & Diana Kusumastuti & Alan Nicholson, 2019. "Establishing Collection and Delivery Points to Encourage the Use of Active Transport: A Case Study in New Zealand Using a Consumer-Centric Approach," Sustainability, MDPI, vol. 11(22), pages 1-23, November.
    13. Carling, Kenneth & Han, Mengjie & Håkansson, Johan & Rebreyend, Pascal, 2015. "Testing the gravity p-median model empirically," Operations Research Perspectives, Elsevier, vol. 2(C), pages 124-132.
    14. Carling, Kenneth & Han, Mengjie & Håkansson, Johan & Rebreyend, Pascal, 2013. "An Empirical Test of the Gravity p-Median Model," HUI Working Papers 90, HUI Research.
    15. Gaigné, C. & Hovelaque, V. & Mechouar, Y., 2020. "Carbon tax and sustainable facility location: The role of production technology," International Journal of Production Economics, Elsevier, vol. 224(C).
    16. Stolletz, Raik & Stolletz, Lars, 2008. "Linearisierungsverfahren für Standortplanungsprobleme mit nichtlinearen Transportkosten," Hannover Economic Papers (HEP) dp-388, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    17. Maciej Drwal & Jerzy Jozefczyk, 2014. "Decomposition algorithms for data placement problem based on Lagrangian relaxation and randomized rounding," Annals of Operations Research, Springer, vol. 222(1), pages 261-277, November.
    18. Kenneth Carling & Mengjie Han & Johan Håkansson & Pascal Rebreyend, 2015. "Distance measure and the $$p$$ p -median problem in rural areas," Annals of Operations Research, Springer, vol. 226(1), pages 89-99, March.
    19. Dong Liang & Wilbert E. Wilhelm, 2013. "Dual‐ascent and primal heuristics for production‐assembly‐distribution system design," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 1-18, February.
    20. Boyacı, Burak & Geroliminis, Nikolas, 2015. "Approximation methods for large-scale spatial queueing systems," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 151-181.

    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:coopap:v:79:y:2021:i:3:d:10.1007_s10589-021-00283-6. 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.