## 2 Related Works  
Due to limited energy and communication ability of wireless sensor nodes, a number of energy-efficient routing protocols have been proposed to prolong their lifetime [10]. Some approaches select cluster heads according to residual energy of sensor nodes [11, 12]. Others transmit data packets by finding the shortest or the most reliable path between any paired nodes [13-15]. A detailed review of energy-efficient protocols is given as follows. The low-energy adaptive cluster hierarchy (LEACH) [4] is one of the most well-known routing protocols to date. LEACH chooses cluster heads in a network to collect the data transmitted by remote sensor nodes. With data fusion and aggregation functions, the cluster heads are able to combine and compress the sensed data into significantly smaller-sized packets. Since the sensed data is fused in each hop, the energy consumption caused by radio transmission can be greatly reduced. [PERSON] _et al._ modified the cluster-head selection algorithm originated from the LEACH protocol to reduce the overall energy consumption of the network [11]. The algorithm takes the residual energy of nodes into account when selecting a proper cluster-head, and also improves the energy-balancing of the network that contributes to prolong the network lifetime. In [12], they further utilize node proximity that allows sensor nodes to join the closest cluster-head in order to minimize the communication cost inside the cluster. However, in [4, 11, 12], the cluster heads transmit sensed data to a base station (BS) directly, and the long distance transmissions consume greater energy. By transmitting the sensed data to the BS using a multi-hop mechanism, the energy consumption of each sensor node can be further reduced. Another protocol focusing on energy-efficiency, the energy-efficient unequal clustering (EEUC) protocol [16], used a multi-hop transmission mechanism to connect cluster heads and a BS. It utilized an unequal probability density to select cluster heads to reduce the loading of nodes near the BS. The power efficient gathering algorithm in sensor information systems (PEGASIS) [17], also emphasizing the idea of reducing energy consumption, allows the sensor nodes to have communication capability to transmit the sensed data to the BS. The PEGASIS minimized the energy consumption of sensor nodes by selecting only one cluster-head in each round. Both EEUC and PEGASIS protocols have been found to outperform the LEACH protocol. The focus of these famous algorithms is to reduce overall energy consumption of the network, so the network lifetime can be extended. However, the full sensing coverage at any given time during a sensing phase is not guaranteed, unless the sensor nodes are equally distributed. In many practical applications, sensor nodes are not equally distributed over the monitoring area, and thus the sensing coverage is hard to maintain under such a circumstance [8]. This drawback would cause a great number of coverage holes, which makes the algorithms unsuitable for mission-critical applications. The coverage-time concept was proposed in [15], where the energy-balancing is taken into consideration in intra- and inter-cluster communications. In this protocol, the cluster-head chooses the shortest hop-count path for the data transmission in inter-cluster, and the sizes of all clusters are the same for energy-balancing. Moreover, [PERSON] [18] presented a coverage-preserving routing protocol, named \"LEACH-Coverage-U\". In contrast with the aforementioned protocols, the LEACH-Coverage-U protocol calculated the overlap sensing areas of all sensor nodes and then selected cluster heads starting from the nodes in a highly overlapped area. The simulation results showed that the LEACH-Coverage-U protocol could prolong the network lifetime compared with existing protocols. Moreover, the coverage and connectivity aware routing protocol based on neural networks was proposed in [19].