中文摘要：

为了延长网络生命期，无线传感器网络必须高效地消耗电池能量，而网络拓扑作为上层协议的重要平台，是实现这一目标的支撑基础．WSN的一个显著特征即具有应用多样性，为了研究符合低概率事件场景的传感器网络拓扑控制方案，建立并分析了传感器网络模型．由于在低概率事件场景下节点侦听能耗占据主导地位，经研究发现此时生命期目标与k-中心问题本质上具有密切联系，可视为k-中心问题的对偶问题，因此针对分簇机制分别设计了3个阶段执行：邻居信息获取阶段、簇头确定阶段和节点归属阶段，从而引入了一种基于k-中心问题的周期性分簇控制算法PCA，PCA算法体现了负载均衡的思想，同时尽可能减少了簇头数目．模型理论分析和仿真实验结果都表明，PCA算法能得到快速部署，并且PCA算法能获得较优的拓扑结构，有效地延长了WSN的生命期．

英文摘要：

In order to fulfill the task of prolonging network lifetime, the primary objective of wireless sensor network execution is to consume the battery energy efficiently. The network topology, which is the important foundation of upper layer protocols, serves as the supportive groundwork for this goal. A significant feature of WSN is application diversity; therefore the topology control techniques under different event scenarios should be obviously different. In searching for a topology control scheme that conforms to the low probability event scenario, a theoretical model of sensor networks is constructed and analyzed. Because the listening cost is the dominating power cost under the low probability event scenario. It turns out that there is consanguineous relationship between network lifetime and the k-center problem, which are dual to each other in the theoretical sense. A periodical clustering algorithm （PCA） based on k-center problem is introduced consequently. PCA is composed of three phases： neighbor discovery phase, head decision phase and node attachment phase. PCA algorithm reflects the thinking of the load balancing, while minimizing the number of cluster heads. The performance of PCA algorithm is analyzed through theoretical model and simulation experiments, which indicates that PCA algorithm can be deployed quickly, and a well-constructed topology and an effectively prolonged network lifetime can be acquired.