In this paper, we study approximation algorithms for the problem of maximum weighted target cover with distance limitations (MaxWTCDL). Given n targets \(T=\left\{ t_{1},t_{2},\ldots ,t_{n}\right\} \) on the plane and m mobile sensors \(S=\left\{ s_{1},s_{2},\ldots ,s_{m}\right\} \) randomly deployed on the plane, each target \(t_i\) has a weight \(w_{i}\) and the sensing radius of the mobile sensors is \(r_{s}\), suppose there is a movement distance constraint b for each sensor and a total movement distance constraint B, where \(B>b\), the goal of MaxWTCDL is to move the mobile sensors within the distance constraints b and B to maximize the weight of covered targets. We present two polynomial time approximation algorithms. One is greedy-based, achieving approximation ratio \(\frac{1}{2v}\) in time \(O(mn^2)\), where . The other is LP-based, achieving approximation ratio \(\frac{1}{v}(1-e^{-1})\) in time \(T_{LP}\), where \(T_{LP}\) is the time needed to solve the linear program.

在本文中，我们研究了具有距离限制的最大加权目标覆盖问题（MaxWTCDL）的近似算法。给定平面上的n 个目标\(T=\left\{ t_{1},t_{2},\ldots ,t_{n}\right\} \)和m 个移动传感器\(S=\left\{ s_ {1},s_{2},\ldots ,s_{m}\right\} \)随机部署在平面上，每个目标\(t_i\)有一个权重\(w_{i}\)和感知半径移动传感器的数量为\(r_{s}\) ，假设每个传感器都有一个移动距离约束b和一个总移动距离约束B，其中\(B>b\)，MaxWTCDL 的目标是移动在距离限制b和B内移动传感器，以最大化覆盖目标的重量。我们提出了两种多项式时间近似算法。一种是基于贪婪的，在时间\(O(mn^2)\)内实现近似比率\(\frac{1}{2v}\)，其中 .另一种是基于 LP 的，在时间\(T_{LP}\)上实现近似比率\(\frac{1}{v}(1-e^{-1})\)，其中\(T_{LP} \)是求解线性规划所需的时间。