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A note on the minimum power partial cover problem on the plane
Journal of Combinatorial Optimization  (IF1.262),  Pub Date : 2022-06-11, DOI: 10.1007/s10878-022-00869-8
Han Dai, Bin Deng, Weidong Li, Xiaofei Liu

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 \(p(s)=c\cdot r(s)^{\alpha }\). The minimum power partial cover problem, introduced by Freund (Proceedings of international workshop on approximation and online algorithms, pp 137–150. 2011., is to determine the power assignment on every sensor such that at least k (\(k\le n\)) points are covered and the total power consumption is minimized. By generalizing the method in Li (Journal of Com. Opti.2020. whose approximation ratio is \(3^{\alpha }\) and enlarging the radius of each disk in the relaxed independent set, we present an \(O(\alpha )\)-approximation algorithm.