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

Menghong Li, Yingli Ran () and Zhao Zhang ()
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Menghong Li: Zhejiang Normal University
Yingli Ran: Zhejiang Normal University
Zhao Zhang: Zhejiang Normal University

Journal of Combinatorial Optimization, No 0, 11 pages

Abstract: Abstract In this paper, we study the minimum power partial cover problem (MinPPC). Suppose X is a set of points and $${\mathcal {S}}$$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 $$p(s)=c\cdot r(s)^\alpha $$p(s)=c·r(s)α. Given an integer $$k\le |X|$$k≤|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 $$3^{\alpha }$$3α. This ratio coincides with the best known ratio for the minimum power full cover problem, and improves previous ratio $$(12+\varepsilon )$$(12+ε) for MinPPC which was obtained only for $$\alpha =2$$α=2.

Keywords: Power; Partial cover; Primal dual; Approximation algorithm (search for similar items in EconPapers)
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DOI: 10.1007/s10878-020-00567-3

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