## 5 Description of Algorithms 1 and 2  
In this section, Algorithms 1 and 2 for inter-node and path adjustment are described in detail; first, the _BM_ are decided for forwarding and receiving acknowledgment for relay and sensor nodes, in which each '_BM_' contains next node's information with its correspondent coordinates to determine the location and distance of nodes. All this information is simultaneously updating in the routing table as [28; 29; 30]. To add the next node, the mechanism of parity flag is introduced if it is 1, then forwarder nodes with all their adjacency are added to set out the packet orientation, and ignored if it is 0. The path should be modified (due to the rotational mechanism technique used in ROBINA) if the \(P_{\text{ACK}}\) does not receive from adjacent nodes as described in Equation (2). The modified \(P_{\text{ACK}}\) is used to set down the path in the desired direction, as mentioned in Algorithm 1. The delivery of data using path adjustment only considers the next forwarder nodes and their re-scheduling. If the distance of nodes does not have a minimum value for sink nodes and the next forwarder nodes, then adjacent nodes will be put up as the next forwarder node and all other nodes are rescheduled by avoiding the void nodes to make the path clear for the destination. In Figure 3, the whole network is divided into three sections: a horizontal region, a vertical region, and a diagonal region, respectively. According to our proposed techniques, three types of nodes make communication possible: relay nodes, sensor nodes, and gateways nodes. The PA-ROBINA mechanism is accordingly adjusted with the help of relay nodes. If void nodes want to become network members, the inter-node adjustment mechanism is activated, and the path is adjusted according to inter-node placement. This mechanism is described with distance in Figure 4 In addition, Algorithm 2 is discussed with data delivery using the PA of ROBINA. For this, the area of path adjustment via relay and inter-nodes is decided. Suppose nodes are present within the path's defined area. In that case, the path is rescheduled according to the role of inter-node adjustment, and data packets are forwarded to the destination's desired direction. In Table 1, all the acronyms with their descriptions are listed. In addition, the flowchart of ROBINA and its variants like PA-ROBINA and PL-ROBINA are described in Figure 5 and Figure 6, respectively. Figure 4: The woring of PA-ROBINA in acoustic scenario. \begin{table} \begin{tabular}{c c} \hline \hline _Acronym_ & _Description_ \\ \hline _Selop_ & _Selection operator_ \\ \hline \(B\) & _Beacon message_ \\ \hline _Dn_ & _Number of dead nodes_ \\ \hline _SNN_ & _Sink neighboring nodes_ \\ \hline _Ns_ & _Set of neighboring nodes_ \\ \hline _Sn_ & _Set of nodes_ \\ \hline _PACK_ & _Packer acknowledgment_ \\ \hline _AdjNi_ & _Adjacency of node_ \\ \hline _Node location_ (N\({}_{i}\)) & _Node location_ \\ \hline _E(Ni)_ & _Energy of node_ \\ \hline _SNN(range)_ & _Range of sink neighboring nodes_ \\ \hline \hline \end{tabular} 
\begin{tabular}{c} \hline \hline B: Beacon message having next node \\ \hline Dn: Set of Dead Nodes \\ \hline S: Sonobuoys \\ S\({}_{n}\): Set of Nodes \\ \hline Parity Flag Values: 0 and 1 (Used to Check Void Nodes) \\ X. Y.