# Robust Evolutionary-Game-Based Routing for Wireless Multimedia Sensor Networks
## 4 EGR Protocol
### Data Redundancy Avoidance and EGR Routing Algorithm  
In the previous sections, we discussed the overlapped regions of FoV created because of the closely placed multimedia sensor nodes. We also introduced the term threshold \(T\), which is a certain portion (for our case, we assume it to be half) of the isosceles triangle of the FoV. The congruent sides of the triangle are denoted by \(\mathsf{C_{8}}\). According to our observations, if any object falls in the FoV of two closely placed sensor nodes and the FoVs of them creates a polygon, the data will be redundant if both  
Figure 9: Utility for choosing variant strategies in the designed game. nodes send the snapshot of the object. If any object falls within the shaded region shown in Figure 10, the FoVs for that object to node 1 and node 2 are almost similar. For geometric shapes like triangle and quadrilateral, we cannot be sure if the overlapped area is big enough to cross the threshold value (\(T\)), or small enough to be under the threshold. The triangles or quadrilaterals created because of the overlapped FoVs can be small or big. Figure 11a,b shows such kind of observations. Based on all these assumptions and interpretations, our data redundancy avoidance algorithm is as follows:  
Figure 11: Different sizes of (**a**) triangles and (**b**) quadrilaterals created because of the overlapped FoVs. Figure 10: Different types of polygons created by the overlapped FoVs of two closely placed sensor nodes: (**1**) sensor nodes placed vertically opposite to each other; (**2**) sensor nodes placed horizontally opposite to each other; (**3**) Sensor nodes placed closely to the left side of their orientation; (**4**) Sensor nodes placed closely to the right side of their orientation. Algorithm 1 basically presents how redundant data between two nodes are dealt with. First, two nodes ofn\({}_{1}\) and n\({}_{2}\) are initialized. R\({}_{1}\) and R\({}_{2}\) are declared as residual energy levels of n\({}_{1}\) and n\({}_{2}\), respectively. We discussed the area threshold T earlier in Section 4.1 while discussing the cluster formation procedure. The threshold is also needed in this algorithm. If the distance between the two nodes is two times greater than the congruent sides of the FoV created by them, it is impossible to have a FoV overlap. Figure 12 presents a scenario where two nodes have a distance that is two times more than the congruent sides of the triangles created due to FoV. If the case is not as in Figure 12, we can conclude that there is a possibility of data redundancy. In this algorithm, we consider data to be redundant if the area created by the two FoVs overlaps to form a  
Figure 12: Scenario where two nodes have a distance that is two times more than the congruent sides of the triangles created due to FoV. polygon. If it forms either a triangle or a quadrilateral, we must compute its area and compare it with the threshold to determine if the data is redundant. If a view of an object is observed to be same for two nodes, the node with higher energy will win the FoV and transmit the data to CH. In Figure 13, from two nodes ofn\({}_{1}\) and n\({}_{2}\), the one that has higher residual energy will win the FoV of the object that is represented as a rectangular box in the figure. The data redundancy avoidance algorithm and optimal CH selection procedure using EG are the core mechanisms of the proposed EGR routing protocol. The entire routing process can be viewed in Figure 14:  
EGR's architecture is similar to that of LEACH; however, the core differences are: (1) cluster formation using the FoVs of the multimedia sensor nodes, (2) data redundancy avoidance using the overlapped FoVs of the sensors, and (3) optimal CH election using EG. The algorithm for our routing process is as follows:  
Figure 14: Overall process for routing in the proposed EGR. Figure 13: A scenario where two nodes have a distance that is less than two times of the congruent sides of the triangles created due to FoV.