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

Han Dai, Bin Deng, Weidong Li () and Xiaofei Liu
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Han Dai: Yunnan University
Bin Deng: Yunnan University
Weidong Li: Yunnan University
Xiaofei Liu: Yunnan University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 2, No 5, 970-978

Abstract: 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.

Keywords: Power partial cover; Primal dual; Approximation algorithm; Relaxed independent set (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-022-00869-8

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