An improved PTAS for covering targets with mobile sensors

IF 0.9 4区 数学 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Journal of Combinatorial Optimization Pub Date : 2025-01-20 DOI:10.1007/s10878-024-01253-4
Nonthaphat Wongwattanakij, Nattawut Phetmak, Chaiporn Jaikaeo, Jittat Fakcharoenphol
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Abstract

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.

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一种用于移动传感器覆盖目标的改进PTAS
本文研究了移动传感器的运动最小化问题。给定一组n个点目标,k- sink最小运动目标覆盖问题是调度最初位于k个基站的移动传感器覆盖所有目标,使传感器的总移动距离最小化。我们提出了一个多项式时间近似方案,用于寻找在时间\(n^{O(1/\epsilon )}\)上运行的这个问题的\((1+\epsilon )\)近似解,当k,基站的数量,是恒定的。我们的算法在没有任何目标分布假设的情况下,以指数方式提高了运行时间\(n^{O(1/\epsilon ^2)}\)。为了设计一种更快的算法,我们证明了最优解中任何单位面积上传感器数量的强界,并采用了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。
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来源期刊
Journal of Combinatorial Optimization
Journal of Combinatorial Optimization 数学-计算机:跨学科应用
CiteScore
2.00
自引率
10.00%
发文量
83
审稿时长
6 months
期刊介绍: The objective of Journal of Combinatorial Optimization is to advance and promote the theory and applications of combinatorial optimization, which is an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communication networks, and management science. It includes complexity analysis and algorithm design for combinatorial optimization problems, numerical experiments and problem discovery with applications in science and engineering. The Journal of Combinatorial Optimization publishes refereed papers dealing with all theoretical, computational and applied aspects of combinatorial optimization. It also publishes reviews of appropriate books and special issues of journals.
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