# Energy-Efficient Connected-Coverage Scheme in Wireless Sensor Networks
## 1 Introduction  
The wireless sensor network (WSN) that is composed by many sensor nodes is applied to many fields, such as environmental monitoring, military reconnaissance, and so on [1, 2]. These sensor nodes distribute in remote areas and they are responsible for sensing and data transmission, which consume lots of energy [3, 4]. In practice, the battery capacity of the sensor node is limited and the realization of the energy replenishment is difficult [5, 6]. To prolong the lifetime of the network, the limited energy of the sensor node should be utilized more efficiently. In WSN, the lifetime of the network is often defined as the longest time that sensor nodes remain connected under the premise of ensuring network coverage. The target coverage is one of typical coverage categories, and multiple monitored target points (MTPs) coverage is an important realization way of the target coverage [7]. A large number of sensor nodes is used to detect these MTPs and transmit sensed data to the sink in order to obtain accurate and detailed data [8]. Generally, more sensor nodes sensing the same MTP means better coverage quality. However, using too many sensor nodes to monitor the same MTP will cause more redundant sensing data, which is wasteful and inefficient for the energy of the sensor node. If the number of the sensor node sensing the same MTP is reduced, then the corresponding sensing data are reduced. Subsequently, the energy that is consumed by sensing and transmission is also reduced. Additionally, these reduced sensor nodes can turn to sleep. When some sensor nodes are depleted, these sleeping nodes can be awakened to replace the exhaustedsensor nodes and keep the coverage of the network. The network lifetime is prolonged. Hence, under the condition of the adequate network coverage, let all MTPs be covered by minimum number of sensor nodes, which is an efficient way of optimizing the network lifetime. Selecting the minimum number of sensor nodes to cover all MTPs has proved to be an NP-hard problem, which is also named as SCP (the set covering problem) [9]. In some works [10; 11; 12], the sensor node scheduling algorithms are proposed in order to reduce redundant sensor nodes, the energy wasted on the redundant coverage can be reduced significantly. However, these algorithms are highly complex and usually cannot obtain the optimal solution. That is, there is still small redundancy in the network. Furthermore, they did not consider the connectivity of the network, the nodes found in the minimum coverage set may not be able to communicate with each other. To address above problem, in the paper we proposed an algorithm based on the genetic algorithm to find the first minimum connected coverage set in an iterative manner. With the network running, the relevant sleeping nodes are constantly awakened according to the remaining energy and replace the dead nodes while ensuring the minimum number of working nodes. The lifetime of the network is effectively extended. The proposed algorithm can be easily extended to the rechargeable WSN. The routing selection is also an important factor that influences the energy efficiency of the data transmission. A higher energy efficiency routing protocol can reduce energy consumption and improve the network lifetime [13]. Organizing sensor nodes into clusters can effectively reduce the number of data transmission and, thus, reduce energy consumption, especially in large scale WSN. Many energy-efficient routing protocols are designed on the basis of a cluster structure. In [14; 15], the authors proposed efficient algorithms to establish the optimal routing protocol, and the energy consumed on routing can be reduced. However, the energy of the sensor node is not considered when selecting the cluster head. If the energy of the node is very low, being selected as the cluster head will accelerate its death. In addition, the distance between the node and base station is not considered.