# An Enhanced Distributed Data Aggregation Method in the Internet of Things
## 3 Proposed Method (LA-RPL)
### Network Graph Formation Phase  
RPL graph is generally challenged by the unbalanced work-load and the degree of network nodes. To address this issue, a k degree constraint is determined in order to prohibit each parent node from \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Definition** & **Variables** & **Definition** \\ \hline \(G\) & Graph & DIS & \begin{tabular}{c} DODAG Information \\ Solicitation \\ \end{tabular} \\ \hline \(V\) & V is a set of vertices & DAO-Ack & \begin{tabular}{c} Destination Advertisement \\ Object Acknowledgement \\ \end{tabular} \\ \hline \(E\) & E is a set of edges & \(\{\alpha,\,\beta,\,p,\,T\}\) & Automata’s operations \\ \hline \(S\) & Set of nodes & \(\alpha\) & Action of Automata \\ \hline \(B\) & Border routers & \(\beta\) & Input set of automata \\ \hline \(u,v\) & Node in graph & \(c\) & Penalties of Automata \\ \hline \(p\) & Parent node & \(d\) & Bonuses of Automata \\ \hline \(p^{\prime}\) & Alternative parent node & \(p\) & Probability of Automata \\ \hline DODAG & \begin{tabular}{c} Destination Oriented Directed \\ Acyclic Graph \\ \end{tabular} & \(T\) & Learning Algorithm \\ \hline GeoRank & \begin{tabular}{c} A geographic routing approach \\ for RPL \\ \end{tabular} & lbl – indicator & Aggregation label \\ \hline Root & Root node of graph (Sink) & \(F\) & Aggregation Function \\ \hline Rank & \begin{tabular}{c} Number hops of Root node in a \\ DODAG \\ \end{tabular} & \(P_{Agg}\) & \begin{tabular}{c} Probability of Aggregation by \\ node \\ \end{tabular} \\ \hline OF & Objective Function & \(P_{AN}\) & \begin{tabular}{c} Number of data packets \\ aggregated by previous nodes \\ \end{tabular} \\ \hline DPP & DODAG Preferred Parent & \(P_{AM}\) & \begin{tabular}{c} Number of data packets not \\ being aggregated by previous \\ nodes \\ \end{tabular} \\ \hline DRL & DODAG Root List & \(RS\) & Reinforcement Signal \\ \hline \(k\) & Constant K is degree of graph & Rate \(j\) & Rate of input packets \\ \hline DIO & DAG Information Object & \(N_{PK_{i}}\) & \
\begin{tabular}{c} Number of aggregated data \\ packets in i \\ \end{tabular} \\ \hline DAO &
\begin{tabular}{c} Destination Advertisement \\ Object \\ \end{tabular} & PDR & Packet Delivery Ratio \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of variables used in the paper. possessing more than (k) threshold children. It is axiomatic that this approach increases the graph levels. An example of the RPL structure and unbalanced network nodes is illustrated in Figure 5[27]. For instance, the constraint of degree k = 2 in the connected structure of the network tree is depicted in Figure 6. According to [40] the queueing mechanism of network nodes has limited efficiency on network congestion reduction. However, the act of increasing network graph levels restricts the number of assigned children to a common parent node and reduces the probability of collision and queue overflow in the network as a result. After the placement of network nodes in the environment, the root node determines the type of objective function, based on the priority of the network application type; then, the node broadcasts the degree restriction value (i.e., k constant) through DIO messages throughout the network [27]. Note that the priority of the network application type specifies the targeted end-to-end delay and packet delivery ratio. Having received the DIO message in the first level, each child node investigates the value of graph degree restriction (written in the Options field of DIO message) to verify whether or not this value exceeds the determined threshold. This value must not exceed the determined threshold. We have used this field in the DIO control message to specify graph and threshold. In other words, this field has not added any overhead to the network but has been able to inform one of the target network functions in the formation of the graph to the members of the graph.