## 5 The Tri-Angular Nearest Vector-Based Energy Efficient Routing (TANVEER)
### Energy Efficient Nearest Vector Selection  
Nearest vector selection is based on the number of nodes and angle calculation, as discussed earlier. The angle will be calculated in three consecutive adjacent directions. The movement of the angle vector is only selected when there is the next forwarder node, and its neighbor node is available without any empty zone. The next forwarder node further computes the angle again and repeat the aforementioned process in order to avoid the empty nodes. Energy is an essential part of underwater communication, especially in the IoT enabled environment [56]. Due to acoustic communication, the nodes are deprecated their energy value continuously. Furthermore, mobile water and dynamic topology alsohave an effect on the overall health of the network. As the path becomes longer by selecting the number of nodes towards the sonobuoys, then the nearest vector path is selected. It is because; by computing the angle thrice only those nodes are selected that cover the angled cone and have the next link with forwarder nodes Moreover, a detailed survey of underwater ad hoc networks is presented in [46; 47; 48; 49] where various methods of underwater communication are discussed. For every nearest vector it selects according to the availability of the node '\(Nv\)', and angle coordinates '\(A(x,y,z)\)', in such a way that '\(Nv\in A\) (\(x,y,z)\)' but not empty regions '\(Nv\
exists Er\)' towards the '\(Sn\)', Equation (4) becomes:  
\[Sn=Nv*A\ (xyz)\ \cup\ Nv\
exists Er\ \gets P_{\text{ACK}} \tag{4}\]  
After the selection of nearest vectors from the set of nodes, the routing path is established towards the sonobuoys, near to it, if the sudden node dies and is able to create the '\(Er\)', the routing path is changed to '\(P_{CHG}\)' and calculates the angle once again. The '\(P_{CHG}\)' mechanism is defined as it is the alternate adjustment for routing path while the next forwarder acknowledges even received the '\(Nv\)' nodes, and its frequency '\(f\)' is the proper set of '\(Tn\)'. If '\(Tn\)' is less than '\(Nv\)', the '\(Sn\)' directly available to receive the packet such that '\(Nv\propto f\)' and according to the path selection mechanism, so the difference '\(D\)' between the nearest sonobuoys and the node is basically as in Equation (5):  
\[D\ (Sn)=(N(l_{n}-l_{1})\rightarrow\varphi\ (fn\cap Tn) \tag{5}\]  
\(P_{CHG}\) will be implemented through the expression as in Equation (6):  
\[P_{CHG}=Pack\ \leftrightarrow Sn\ :\ \exists\ \sum_{n}^{0}minNv*\forall\ f(Nv*(1-Tn\ \oint_{l=0}^{\#}fn(Er\frac{\pi}{2}*(A\ (x,y,\ z)) \tag{6}\]  
It is a bi-conditional structure that means the path does not change if and only if the '\(ACK\)' is continuously received with sonobuoys '\(Sn\)'. The available nodes from '\(0\)_to_Nv\)' the minimum selection of total frequency of nodes '\(f\)' is subtracted with 1 from the total number of nodes by calculating the angle coordinates to change the path '\(P_{CHG}\)'. Ultimately it sets the path change, and the route again receives the packet from the node (1 is used for this node that holds the data packet before getting the node of the empty region). Meanwhile, by changing the path, it has the opportunity to select more nodes to forward the data packet further; the detail of this strategy is discussed in Algorithms 1 and 2. Additionally, if the nodes cannot be selected (or there is no availability) at the top of the layer near to water surface, the packet is discarded, and the alternate novel approach is used as discussed in Algorithm 3, in which extra watchman nodes are deployed around the edges and near the sonobuoys to rescue the discarded data packets and minimize the occurrence of packet loss ratio.