## 2 Related Work  
The introduction of mobile sinks in WSNs has gained more and more attention to balance energy consumption and prolong network lifetime. In 2005 and 2006, some predefined sink movement trajectories were studied. In [5], the authors investigated the benefits of a heterogeneous architecture for WSNs composed of a few resource-rich mobile nodes and a large number of simple static nodes. They studied WSNs with one mobile sink and one mobile relay individually. In [6], the authors studied a base station which moves along a predetermined movement path to collect data from cluster heads (CHs). Sensor nodes which were closest to mobile sink trajectory will be chosen as CHs, and CHs sent data to mobile node as it passed by. In [7], the authors proposed a hierarchical cluster-based data dissemination scheme called HCDD to disseminate data to mobile sinks with light control overhead. In HCDD, sensor nodes found the route without the location information of sensor nodes, and HCDD operated without using any expensive and power-consuming GPS device to estimate the location information. This was the first attempt to utilize single mobile sinks to achieve better network performance, and the sink moving strategies are mostly intuitive and simple. In 2008, the optimal sink movement trajectory was further studied. In [8], the authors first explored and categorized the general problem of sink mobility in the context of trade-offs between data delivery delay and network lifetime. Then they studied a novel mobility control solution in which sensor nodes cooperatively determine the sink trajectory, and navigate mobile sinks for delay and energy optimized data collection. In [9], the authors proposed a data dissemination protocol and defined a vertical line that divides the sensor field into two equal parts. This line acted as a rendezvous area for data storage and look up. In [10], the authors focused on the problem of finding an optimal path of a mobile device to achieve the smallest data delivery latency in the case of minimum energy consumption at each sensor node. They demonstrated that their algorithm successfully finds the paths that result in 10%-50% shorter latency compared to previously proposed methods. During this stage, some early theoretical work to find optimal sink moving trajectories was performed with certain constraints. However, the authors also mainly dealt with single sink node based on their own devising scenarios, some of which were not feasible to practical application. In 2010 and 2011, sink mobility technology drew much more attention with deeper study. In [11], the authors studied the backbone-based virtual infrastructure (BVI) to avoid the routing structure construction per each mobile sink by full network flooding. On that basis, they proposed a novel BVI-based communication protocol and showed that their proposed protocol was superior to the existingprotocols in terms of the control overhead and the data delivery hop counts. In [12], the authors first investigated the optimum routing strategy for the static sensor network, and then further proposed a number of motions stratified for the mobile sinks to gather real time data from static sensor network, with the objective of maximizing the network lifetime. In particular, they considered a more realistic model where the moving speed and path for mobile sinks are constrained. In [13], the authors proposed a novel geographic routing for mobile sinks. The proposed scheme took advantage of the wireless broadcast transmission nature of sensor nodes. With the moving of the sink node, the new location information was propagated along the reverse geographic routing path to the source during data delivery. The authors proposed a data collection scheme, called the maximum amount shortest path (MASP) which increased network throughput and conserved energy by optimizing the assignment of sensor nodes [14]. MASP was formulated as an integer linear programming problem and solved based on genetic algorithm.