In wireless sensor networks, sensor nodes closest to the base station are critical for the lifetime of the sensor network because these nodes need to relay more packets than nodes further away form the base station. Forming clusters can save energy, and mitigate hot spot problem at some extent. However, cluster head near to the base station are also prone to die. Besides, the cluster head is much more expensive than ordinary nodes. In this paper, we optimize the number of cluster heads by least coverage model. On this basis, we study that adding a limited number of cluster heads to a sensor ne...