In this paper, we consider the wireless sensor network in which the power of each sensor is adjustable. Given a set of sensors and a set of targets, we study a problem of minimizing the total power such that the coverage of targets meets partial multi-cover requirement, that is, there are at least a given number of targets each covered by a given number of sensors (this number is called the covering requirement for the target). This is called the minimum power partial multi-cover problem (MinPowerPMC) in a wireless sensor network. Under the assumption that the covering requirements for all targets are upper bounded by a constant, we design the first PTAS for the MinPowerPMC problem, that is, for any \(\varepsilon >0\), a polynomial-time \((1+\varepsilon )\)-approximation.

在本文中，我们考虑了其中每个传感器的功率均可调的无线传感器网络。给定一组传感器和一组目标，我们研究使总功率最小化的问题，以使目标的覆盖范围满足部分多重覆盖的要求，即，至少存在给定数量的目标，每个目标均被给定覆盖传感器的数量（此数量称为目标的覆盖要求）。在无线传感器网络中，这称为最小功率部分多重覆盖问题（MinPowerPMC）。假设所有目标的覆盖要求均以一个常数为上限，我们针对MinPowerPMC问题（即对于任何\（\ varepsilon> 0 \），多项式时间）设计第一个PTAS。\（（（1+ \ varepsilon）\） -近似值