## 1 Introduction  
Technology advancements in the areas of micro-mechantronic systems and wireless networks, have allowed the rapid development of wireless micro-sensors for wireless communications. Wireless Sensor Networks comprise massive amounts of sensor nodes which make up the network for monitoring the region of interest and feed data about the targets or events of interest back to the end-users. WSNs usually include tiny, inexpensive and resource limited devices which communicate with each other in a multi-hop manner. WSNs can be widely used to perform military tracking and surveillance, natural disaster relief, hazardous environment exploration and health monitoring, _etc._[1; 2; 3]. Due to the fact that it is impractical, if not impossible, to recharge sensor nodes, it is very important to design energy efficient routing algorithms or protocols to improve the energy efficiency of sensors by balancing and minimizing the energy consumption, and thus prolong network lifetime for WSNs [4]. In general, the sources of the energy consumption consist of three parts, namely sensing, processing and communication. We only consider the energy consumption during the communication process due to the fact that to transmit one bit of message consumes around 3,000 times more energy than to process the message. An unbalanced energy assumption phenomenon occurs when the one-hop neighboring sensors deplete their battery power, and those sensors far away may still have more than 90% of their initial energy unused [5; 6; 7]. When comparing with sensors far from the sink, nearby sensors are shared by more sensor-to-sink paths, thus they have heavier message relay loads, and consume more energy [8]. To solve this problem, many energy efficient routing algorithms and protocols have been proposed in recent years, including clustering based routing protocols [9; 10; 11; 12; 13; 14; 15; 16], mobile sink based routing protocols [17; 18; 19; 20; 21; 22], power-aware routing [23; 24; 25] and multi-level transmission radii routing [26]. Clustering has characteristics such as scalable, energy-efficient, lower latency, which make it a popular technique for WSNs. The idea is to select a set of cluster heads from the set of nodes in the network, and then cluster the remaining nodes with these heads [12]. The data gathered are transmitted through cluster heads to remote base stations or sink nodes. However, sink nodes are always fixed, which could result in the neighboring nodes to dying much faster and causing network partition as well as isolated sensors. A typically clustered sensor network is illustrated in Figure 1.  
The use of mobile sinks can potentially provide energy-efficient data collection with well-designed networking protocols for WSNs [27]. When using the mobile sink in practice, the sink nodes can be attached to vehicles, animals or people that can move inside the region of interest. Usually, static sink nodes are not very efficient [28]. Although single hop data collection is feasible in networks deployed in small regions, the multi-hop transmission manner is more commonly used in large sensor areas [29]. Intuitively, mobile sinks gain advantages by mitigating the so-called hot spot problem, balancing energy among sensor nodes, prolonging network lifetime, reducing transmission latency, and improving network performance by periodically accessing some isolated nodes into the network. In this paper, we propose a Mobile sink-based improved algorithm for Stable Election (MSE) with non-uniform node distribution for WSNs. In this improved algorithm, the trajectory of mobile sinks locates in the centre line of the sensing field. Sink nodes move back and forth along the designed trajectory. The network is divided into several clusters based on the Stable Election Protocol (SEP) [30]. Each cluster head collects data and feeds it to the mobile sink. The rest of the paper is organized as follows: Section 2 describes some related work, and our system model is provided in Section 3.