This article deals with reliable and unreliable mobile sensors having identical sensing radius r , communication radius R , provided that r ≤ R and initially randomly deployed on the plane by dropping them from an aircraft according to general random process. The sensors have to move from their initial random positions to the final destinations to provide greedy path k 1 -coverage simultaneously with k 2 -connectivity. In particular, we are interested in assigning the sensing radius r and communication radius R to minimize the time required and the energy consumption of transportation cost for sensors to provide the desired k 1 -coverage with k 2 -connectivity. We prove that for both of these optimization problems, the optimal solution is to assign the sensing radius equal to r = k 1 || E [S]||/2 and the communication radius R = k 2 || E [S]||/2, where || E [S]|| is the characteristic of general random process according to which the sensors are deployed. When r < k 1 || E [S]||/2 or R < k 2 || E [S]||/ 2, and sensors are reliable, we discover and explain the sharp increase in the time required and the energy consumption in transportation cost to ensure the desired k 1 -coverage with k 2 -connectivity.

中文翻译：

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关于无线传感器网络中的范围分配以最小化覆盖连接成本

本文处理具有相同感应半径的可靠和不可靠移动传感器r, 通讯半径R, 前提是r≤R最初是随机部署的在飞机上根据一般随机过程将它们从飞机上丢弃。传感器必须从其初始随机位置移动到最终目的地以提供贪婪路径ķ 1-同时覆盖ķ 2-连接性。特别是，我们有兴趣分配感应半径r和通讯半径R尽量减少所需时间和能源消耗传感器提供所需的运输成本ķ 1- 覆盖ķ 2-连接性。我们证明，对于这两个优化问题，最佳解决方案是将感知半径分配为r=ķ 1||乙[S]||/2 和通讯半径R=ķ 2||乙[S]||/2，其中 ||乙[S]|| 是部署传感器的一般随机过程的特征。什么时候r<ķ 1||乙[S]||/2 或R<ķ 2||乙[S]||/ 2、传感器可靠，我们发现并解释急剧增加在所需的时间和能源消耗中的运输成本，以确保所需的ķ 1- 覆盖ķ 2-连接性。