## 3 Preliminaries
### Network Model  
In our model, a large number of sensor-nodes are being distributed in a large target field which are represented by \(S=\{s_{1},...,s_{n}\}\) with the ability to recognize the events individually. By considering the large-scale of the environment, it is not practical to install the sensor-nodes manually. Therefore, we adopt a random distribution manner such as by aircraft. To conserve energy and for improving the network's security, we assume that the sensor-nodes do not contact with any global positioning system to obtain their accurate locations in the network. Instead, they just contact with their  
Figure 2: An application case for EWSNs with Mobile-Sink.  
neighbor sensor-nodes which are located in their communication range and keep the position by \(PS=\left\{ps_{i}\left(\theta_{i},d_{i}\right)\mid\forall i=1,...,n\right\}\) where \(\theta\) represents the direction of neighbor sensor-node and \(d\) indicates its Euclidean distance. In addition, the following assumptions are being considered in our model [(43; 44; 45; 46; 47)]:  
1. A target field without limitation based on geographical differences.
2. One mobile-sink in the network.
3. The sensor-nodes have enough computational capabilities and are able to run our proposed solution.
4. Each sensor-node has a unique ID which is known for the mobile-sink and the base-station.
5. The sensor-nodes and the base-station are stationary after installation in the target field.
6. The network is homogenous that means all of the sensor-nodes are in the same type. And in the beginning of network's operation, they have the same amount of initial energy.
7. We assume that the conditions of MAC layer are ideal and communication links between sensor-nodes can establish or cannot. In case of establishment, the sensor-nodes can contact with each other with high quality (based on the standards for wireless communication) (This is an ideal assumption which might not be practical in real wireless communication fashion. The reason for this assumption is to facilitate our simulation. Generally, if two sensor-nodes or a sensor-node with the mobile-sink cannot contact with each other based on the expected quality, they will not be considered in the communication range of each other).
8. The sensor-nodes and the mobile-sink are able to control their transmission power to the desired destination (This assumption is arguable in practical implementations. However, the correctness of our assumption just implies that the sensor-nodes can conserve their energy by adjusting their transmission power and operate longer in the network. Our proposed approach does not rely on this assumption).
9. The sensor-nodes and the mobile-sink are able to calculate the distance from the received signal strength (Some scholars might doubt on the possibility of this assumption. Indeed, our approach does not need the accurate distance between the sensor-nodes. It is just important to recognize the neighbor sensor-nodes, correctly).
10. The radio link is symmetric which means energy consumption for data transmission from node A to node B is same as from node B to node A (This assumption is ideal. We relied on this assumption because of facilitating our simulation).
11. We neglect communication time between the sensor-nodes.