Abstract: 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.