Approximation algorithm for minimum power partial multi-coverage in wireless sensor networks

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 ε>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon >0$$\end{document}, a polynomial-time (1+ε)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1+\varepsilon )$$\end{document}-approximation.