This paper considers a movement minimization problem for mobile sensors. Given a set of $n$ point targets, the $k$-Sink Minimum Movement Target Coverage Problem is to schedule mobile sensors, initially located at $k$ base stations, to cover all targets minimizing the total moving distance of the sensors. We present a polynomial-time approximation scheme for finding a $(1+\epsilon)$ approximate solution running in time $n^{O(1/\epsilon)}$ for this problem when $k$, the number of base stations, is constant. Our algorithm improves the running time exponentially from the previous work that runs in time $n^{O(1/\epsilon^2)}$, without any target distribution assumption. To devise a faster algorithm, we prove a stronger bound on the number of sensors in any unit area in the optimal solution and employ a more refined dynamic programming algorithm whose complexity depends only on the width of the problem.

翻译：本文研究可移动传感器的移动最小化问题。给定一组$n$个点目标，k-汇聚点最小移动目标覆盖问题旨在调度初始位于$k$个基站的移动传感器，以最小化传感器总移动距离的方式覆盖所有目标。我们针对该问题提出一种多项式时间近似方案，在$k$（基站数量）为常数时，可找到$(1+\epsilon)$近似解，运行时间为$n^{O(1/\epsilon)}$。与先前需在$n^{O(1/\epsilon^2)}$时间内运行的工作相比，我们的算法将运行时间指数级改进，且无需任何目标分布假设。为设计更快的算法，我们证明了最优解中任意单位面积内传感器数量的更强上界，并采用一种更精细的动态规划算法，其复杂度仅取决于问题的宽度。