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New algorithms for k-center and extensions

Author

Listed:
  • René Brandenberg

    (Technische Universität München)

  • Lucia Roth

    (Technische Universität München)

Abstract

The problem of interest is covering a given point set with homothetic copies of several convex containers C 1,…,C k , while the objective is to minimize the maximum over the dilatation factors. Such k-containment problems arise in various applications, e.g. in facility location, shape fitting, data classification or clustering. So far most attention has been paid to the special case of the Euclidean k-center problem, where all containers C i are Euclidean unit balls. Recent developments based on so-called core-sets enable not only better theoretical bounds in the running time of approximation algorithms but also improvements in practically solvable input sizes. Here, we present some new geometric inequalities and a Mixed-Integer-Convex-Programming formulation. Both are used in a very effective branch-and-bound routine which not only improves on best known running times in the Euclidean case but also handles general and even different containers among the C i .

Suggested Citation

  • René Brandenberg & Lucia Roth, 2009. "New algorithms for k-center and extensions," Journal of Combinatorial Optimization, Springer, vol. 18(4), pages 376-392, November.
    • Handle: RePEc:spr:jcomop:v:18:y:2009:i:4:d:10.1007_s10878-009-9226-9
    DOI: 10.1007/s10878-009-9226-9
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    Citations

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    Cited by:

    1. Hatem Fayed & Amir Atiya, 2013. "A mixed breadth-depth first strategy for the branch and bound tree of Euclidean k-center problems," Computational Optimization and Applications, Springer, vol. 54(3), pages 675-703, April.
    2. Amir Ahmadi-Javid & Pooya Hoseinpour, 2022. "Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2621-2633, September.
    3. Callaghan, Becky & Salhi, Said & Nagy, Gábor, 2017. "Speeding up the optimal method of Drezner for the p-centre problem in the plane," European Journal of Operational Research, Elsevier, vol. 257(3), pages 722-734.

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