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A note on the minimum power partial cover problem on the plane

Author

Listed:
  • Han Dai

    (Yunnan University)

  • Bin Deng

    (Yunnan University)

  • Weidong Li

    (Yunnan University)

  • Xiaofei Liu

    (Yunnan University)

Abstract

Given a set of n points and a set of m sensors on the plane, each sensor s can adjust its power p(s) and the covering range which is a disk of radius r(s) satisfying $$p(s)=c\cdot r(s)^{\alpha }$$ p ( s ) = c · r ( s ) α . The minimum power partial cover problem, introduced by Freund (Proceedings of international workshop on approximation and online algorithms, pp 137–150. 2011. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.737.1320 ), is to determine the power assignment on every sensor such that at least k ( $$k\le n$$ k ≤ n ) points are covered and the total power consumption is minimized. By generalizing the method in Li (Journal of Com. Opti.2020. https://doi.org/10.1007/s10878-020-00567-3 ) whose approximation ratio is $$3^{\alpha }$$ 3 α and enlarging the radius of each disk in the relaxed independent set, we present an $$O(\alpha )$$ O ( α ) -approximation algorithm.

Suggested Citation

  • Han Dai & Bin Deng & Weidong Li & Xiaofei Liu, 2022. "A note on the minimum power partial cover problem on the plane," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 970-978, September.
    • Handle: RePEc:spr:jcomop:v:44:y:2022:i:2:d:10.1007_s10878-022-00869-8
    DOI: 10.1007/s10878-022-00869-8
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    References listed on IDEAS

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    1. Yingli Ran & Xiaohui Huang & Zhao Zhang & Ding-Zhu Du, 2021. "Approximation algorithm for minimum power partial multi-coverage in wireless sensor networks," Journal of Global Optimization, Springer, vol. 80(3), pages 661-677, July.
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    Cited by:

    1. Qian Su & Qinghui Zhang & Xuejie Zhang, 2022. "Energy-Aware Cloud-Edge Collaborative Task Offloading with Adjustable Base Station Radii in Smart Cities," Mathematics, MDPI, vol. 10(21), pages 1-33, October.

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