In this paper we study the min-max cycle cover problem with neighborhoods, which is to find a given number of $K$ cycles to collaboratively visit $n$ Points of Interest (POIs) in a 2D space such that the length of the longest cycle among the $K$ cycles is minimized. The problem arises from many applications, including employing mobile sinks to collect sensor data in wireless sensor networks (WSNs), dispatching charging vehicles to recharge sensors in rechargeable sensor networks, scheduling Unmanned Aerial Vehicles (UAVs) to monitor disaster areas, etc. For example, consider the application of employing multiple mobile sinks to collect sensor data in WSNs. If some mobile sink has a long data collection tour while the other mobile sinks have short tours, this incurs a long data collection latency of the sensors in the long tour. Existing studies assumed that one vehicle needs to move to the location of a POI to serve it. We however assume that the vehicle is able to serve the POI as long as the vehicle is within the neighborhood area of the POI. One such an example is that a mobile sink in a WSN can receive data from a sensor if it is within the transmission range of the sensor (e.g., within 50 meters). It can be seen that the ignorance of neighborhoods will incur a longer traveling length. On the other hand, most existing studies only took into account the vehicle traveling time but ignore the POI service time. Consequently, although the length of some vehicle tour is short, the total amount of time consumed by a vehicle in the tour is prohibitively long, due to many POIs in the tour. In this paper we first study the min-max cycle cover problem with neighborhoods, by incorporating both neighborhoods and POI service time into consideration. We then propose novel approximation algorithms for the problem, by exploring the combinatorial properties of the problem. We finally evaluate the proposed algorithms via experimental simulations. Experimental results show that the proposed algorithms are promising. Especially, the maximum tour times by the proposed algorithms are only about from 80% to 90% of that by existing algorithms.

中文翻译：

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邻域最小-最大循环覆盖问题的逼近算法

在本文中，我们研究邻域的最小-最大循环覆盖问题，即找到给定数量的 $ K $ 协作访问的周期 $ n $ 二维空间中的兴趣点（POI），使得 $ K $ 周期被最小化。该问题源于许多应用，包括使用移动接收器收集无线传感器网络（WSN）中的传感器数据，调度充电车辆以对可充电传感器网络中的传感器进行充电，调度无人飞行器（UAV）来监视灾区等。例如，请考虑采用多个移动接收器来收集WSN中的传感器数据的应用。如果某个移动接收器具有较长的数据收集行程，而其他移动接收器具有较短的行程，则在较长的行程中会导致传感器的数据收集延迟较长。现有研究假设一辆车需要移动到POI的位置才能为其提供服务。但是，我们假设只要车辆在POI的附近区域内，车辆就能为POI服务。一个这样的示例是，如果无线接收器在传感器的传输范围内（例如，在50米之内），则它可以从传感器接收数据。可以看出，社区的无知将导致更长的旅行时间。另一方面，大多数现有研究仅考虑了车辆行驶时间，却忽略了POI服务时间。因此，尽管某些车辆旅行的时间短，但是由于旅行中的许多POI，旅行中的车辆消耗的总时间过长。在本文中，我们首先通过考虑邻域和POI服务时间来研究邻域的最小-最大循环覆盖问题。然后，通过探索问题的组合性质，我们提出了针对该问题的新颖近似算法。我们最终通过实验仿真评估了提出的算法。实验结果表明，该算法是有前途的。特别地，所提出的算法的最大巡回时间仅是现有算法的最大巡回时间的大约80％至90％。