Abstract
In this paper, we study the minimum power partial cover problem (MinPowerPartCov). Suppose X is a set of points and \(\mathcal S\) is a set of sensors on the plane, each sensor can adjust its power, the covering range of a sensor s with power p(s) is a disk centered at s which has radius r(s) satisfying \(p(s)=c\cdot r(s)^\alpha \). Given an integer \(k\le |X|\), the MinPowerPartCov problem is to determine the power assignment on each sensor such that at least k points are covered and the total power consumption is the minimum. We present an approximation algorithm with approximation ratio \(3^{\alpha }\), using a local ratio method, which coincides with the best known ratio for the minimum power (full) cover problem. Compared with the paper [9] which studies the MinPowerPartCov problem for \(\alpha =2\), our ratio improves their ratio from \(12+\varepsilon \) to 9.
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Acknowledgment
This research is supported in part by NSFC (11771013, 61751303, 11531011) and the Zhejiang Provincial Natural Science Foundation of China (LD19A010001, LY19A010018).
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Li, M., Ran, Y., Zhang, Z. (2019). Approximation Algorithms for the Minimum Power Partial Cover Problem. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_17
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