Topology control, including topology construction and maintenance phases, is a vital conception for wireless ad-hoc networks of any kind, expressly the wireless sensor networks (WSN). Topology maintenance, the latter phase, concerns several problems, such as optimizing the energy consumption, increasing the data rate, making clusters, and sustaining the connectivity. A disconnected network, among other strategies, can efficiently be connected again using a Movement-based Connectivity Restoration (MCR) method, where a commensurate number of nodes move (or are moved) to the desired positions. However, finding an optimal route for the nodes to be moved can be a formidable problem. As a matter of fact, this paper presents details regarding a direct proof of the NP-Completeness of the MCR Problem by a reduction of the well-studied Steiner Tree Problem using the minimum number of Steiner points and the bounded edge length.

中文翻译：

---

无线Ad-Hoc和传感器网络中基于运动的连接恢复问题分析

拓扑控制，包括拓扑构建和维护阶段，对于任何类型的无线自组织网络（尤其是无线传感器网络（WSN））都是至关重要的概念。后一阶段的拓扑维护涉及多个问题，例如优化能耗，提高数据速率，建立集群以及维持连接性。除其他策略外，可以使用基于移动的连接恢复（MCR）方法再次有效地断开连接的网络，在该方法中，相当数量的节点移动（或移动）到所需位置。但是，找到要移动的节点的最佳路线可能是一个艰巨的问题。事实上，