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A primal-dual algorithm for the minimum power partial cover problem

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Abstract

In this paper, we study the minimum power partial cover problem (MinPPC). Suppose X is a set of points and \({\mathcal {S}}\) is a set of sensors on the plane, each sensor can adjust its power and the covering range of a sensor s with power p(s) is a disk of radius r(s) satisfying \(p(s)=c\cdot r(s)^\alpha \). Given an integer \(k\le |X|\), the MinPPC problem is to determine the power assignment on every sensor such that at least k points are covered and the total power consumption is the minimum. We present a primal-dual algorithm for MinPPC with approximation ratio at most \(3^{\alpha }\). This ratio coincides with the best known ratio for the minimum power full cover problem, and improves previous ratio \((12+\varepsilon )\) for MinPPC which was obtained only for \(\alpha =2\).

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Acknowledgements

This research is supported in part by NSFC (11771013, 61751303, 11531011, 11901533) and ZJNSFC (LD19A010001, LA19A010018).

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Menghong Li, Yingli Ran & Zhao Zhang

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  1. Menghong Li
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  2. Yingli Ran
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  3. Zhao Zhang
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Correspondence to Yingli Ran or Zhao Zhang.

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Li, M., Ran, Y. & Zhang, Z. A primal-dual algorithm for the minimum power partial cover problem. J Comb Optim 44, 1913–1923 (2022). https://doi.org/10.1007/s10878-020-00567-3

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