障碍物扫描覆盖的近似算法
Approximation Algorithms for Barrier Sweep Coverage
摘要：
时变覆盖，即扫描覆盖是无线传感器网络领域的一个新发展，其中少量的移动传感器周期性地扫描或监测相对大量的位置。在这篇文章中，我们研究了移动传感器的障碍扫描覆盖被认为是一个有限长度的平面上的连续曲线的障碍。曲线上每个点的覆盖率是随时间变化的。我们提出了一个最佳的解决方案，扫描覆盖的有限长度连续曲线。移动传感器的能量来源通常是有限功率的电池，因此能量受限的扫描覆盖对于长时间运行的应用来说是一个具有挑战性的问题。我们提出了一个能量受限的扫描覆盖问题，每个移动传感器必须经常访问一个能源充电或更换电池。我们提出了一个$\frac{13}{3}$ -近似算法。所提出的多曲线算法在特殊情况下实现了最佳逼近因子2。我们针对一般问题提出了一个5-近似算法。作为一组线段的障碍扫描覆盖问题的应用，我们制定了一个数据收集问题。在这个问题中，一组移动传感器任意地监测线段，每个线段一个。一组数据骡子周期性地从该组移动传感器收集监测数据。我们证明了寻找最少数量的数据骡子定期收集数据从每个移动传感器是NP难的，并提出了一个3-近似算法来解决它。
英文摘要：
Time-varying coverage, namely sweep coverage is a recent development in the area of wireless sensor networks, where a small number of mobile sensors sweep or monitor comparatively large number of locations periodically. In this article we study barrier sweep coverage with mobile sensors where the barrier is considered as a finite length continuous curve on a plane. The coverage at every point on the curve is time-variant. We propose an optimal solution for sweep coverage of a finite length continuous curve. Usually energy source of a mobile sensor is battery with limited power, so energy restricted sweep coverage is a challenging problem for long running applications. We propose an energy restricted sweep coverage problem where every mobile sensors must visit an energy source frequently to recharge or replace its battery. We propose a $\frac{13}{3}$-approximation algorithm for this problem. The proposed algorithm for multiple curves achieves the best possible approximation factor 2 for a special case. We propose a 5-approximation algorithm for the general problem. As an application of the barrier sweep coverage problem for a set of line segments, we formulate a data gathering problem. In this problem a set of mobile sensors is arbitrarily monitoring the line segments one for each. A set of data mules periodically collects the monitoring data from the set of mobile sensors. We prove that finding the minimum number of data mules to collect data periodically from every mobile sensor is NP-hard and propose a 3-approximation algorithm to solve it.
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