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A simple greedy approximation algorithm for the minimum connected $$k$$ k -Center problem

Author

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  • Dongyue Liang

    (Xi’an Jiaotong University)

  • Liquan Mei

    (Xi’an Jiaotong University)

  • James Willson

    (University of Texas at Dallas)

  • Wei Wang

    (Xi’an Jiaotong University)

Abstract

In this paper, we consider the connected $$k$$ k -Center ( $$CkC$$ C k C ) problem, which can be seen as the classic $$k$$ k -Center problem with the constraint of internal connectedness, i.e., two nodes in a cluster are required to be connected by an internal path in the same cluster. $$CkC$$ C k C was first introduced by Ge et al. (ACM Trans Knowl Discov Data 2:7, 2008), in which they showed the $$NP$$ N P -completeness for this problem and claimed a polynomial time approximation algorithm for it. However, the running time of their algorithm might not be polynomial, as one key step of their algorithm involves the computation of an $$NP$$ N P -hard problem. We first present a simple polynomial time greedy-based $$2$$ 2 -approximation algorithm for the relaxation of $$CkC$$ C k C —the $$CkC^*$$ C k C ∗ . Further, we give a $$6$$ 6 -approximation algorithm for $$CkC$$ C k C .

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:4:d:10.1007_s10878-015-9831-8
    DOI: 10.1007/s10878-015-9831-8
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    References listed on IDEAS

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    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.
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    1. Lingping Kong & Jeng-Shyang Pan & Václav Snášel & Pei-Wei Tsai & Tien-Wen Sung, 2018. "An energy-aware routing protocol for wireless sensor network based on genetic algorithm," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 67(3), pages 451-463, March.

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