# Robust Evolutionary-Game-Based Routing for Wireless Multimedia Sensor Networks
## 4 EGR Protocol
### Cluster Formation  
Multimedia sensors, such as cameras, have directional views and can capture multimedia data based on that. Multimedia sensor nodes deployed randomly and densely with fixed lenses (having a certain angle) are assumed in this study because most of the existing WMSN platforms (such as SensEye and Panotes) have fixed lenses. It is also assumed that sensors are aware of their positions. All the sensor nodes must be equipped to have the information of their location coordinates and orientation. Any lightweight localization techniques can be used in this case. We mentioned the overlapping area earlier in this study and now would like to introduce a term threshold (\(T\)), which is the minimum percentage of the overlapped region for the FoVs. This threshold will be used to define the cluster formation process. It will denote the minimum percentage of the overlapped region \begin{table}
\begin{tabular}{c c} \hline \hline
**Phase** & **Operation** \\ \hline \multirow{4}{*}{Setup} & (1) Cluster formation. \\  & (2) Intelligent selection of CH nodes using game theory. \\  & (3) CHs advertise to CM. \\  & (4) CMs send join requests to CHs. \\ \hline \multirow{4}{*}{Steady state} & (5) Sink nodes broadcast to CHs. \\  & (6) CHs decide which sink to transmit data based on the RSSI value. \\ \cline{1-1}  & (7) Use of data redundancy avoidance algorithm. \\ \cline{1-1}  & (8) Data transmission. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detailed description if the operations in setup and steady state phase. Figure 2: Setup and steady-state phases of EGR. between the sensor nodes' FoV for membership inclusion in the cluster. Figure 3 shows the FoV of a multimedia sensor node. In Figure 3, we can assume the FoV to be an isosceles triangle having two congruent sides. The vertex angle can be represented as theta (\(\theta\)). The length of the congruent sides can be denoted as \(mn=Cs\). The orientation angle is \(\lambda\). Let us also assume a sensor that is located at point m (\(x_{1},y_{1}\)). To determine the coordinates of \"\(n\)\" and \"\(o\)\" points, the following formulations can be undertaken:  
\[x_{3}=x_{1}+C_{s}\cdot\cos(\lambda). \tag{1}\]  
\[y_{3}=y_{1}+C_{s}\cdot\sin(\lambda). \tag{2}\]  
\[x_{2}=x_{1}+C_{s}\cdot\cos((\lambda+\theta)mod2\pi). \tag{3}\]  
\[y_{2}=y_{1}+C_{s}\cdot\sin((\lambda+\theta)\text{mod}2\pi). \tag{4}\]  
If we know the coordinates of a triangle, it requires only simple matrix operations to compute the area. This is necessary because a certain portion of the area (1/2 or 3/4) of the triangle is to be defined later as threshold in our cluster formation technique and data redundancy avoidance algorithm. There are three possible geometrical shapes that can be noted by observing the overlapping FoVs of two nearby multimedia sensor nodes. They are triangle, quadrilateral, and polygon. Figure 4 shows the different shapes of the overlapped area. The shaded regions represent the overlapped area in the figure. The threshold \(T\) can be defined as half of the area of the triangle created because of the FoV of a sensor node. The nodes that are close to each other, among which the overlapped FoV is greater than the threshold, can be in the same cluster. For example, the nodes shown in Figure 4a cannot belong to  
Figure 4: Different geometric shapes that can be caused because of the overlapped FoV: (**a**) Quadrilateral; (**b**) Triangle; (**c**) Polygon. Figure 3: FoV of a camera in a multimedia sensor node. the same cluster; however, nodes in Figure 4c may belong to the same cluster. For EGR, the algorithm to form the cluster is executed in a centralized way via sink nodes. This centralized architecture was used because of the following reasons:  
* If the architecture is distributed, each node must notify the rest of the nodes about its location and orientation. * The sink nodes can be provided with adequate amount of resources, such as storage and power supply.