# Data Aggregation Based on Overlapping Rate of Sensing Area in Wireless Sensor Networks
## 3 Network Model and Aggregation Rules
### Aggregation Rules
In our experiments, it is rare to achieve this strict condition in networks. Therefore, in general, \(E_{i}^{k}>E_{j}^{k}\). The gathering node selection from the candidate parent node is more energy-efficient than from the neighbor node. For instance, we discuss about how \(v_{3}\) (the current node) selects its gathering node from \(v_{1}\) and \(v_{4}\). In Figure 4, \(L_{3}=2\), \(OR_{1,3}=0.5\), \(OR_{3,4}=0.7\). The total energy cost of transmitting data of \(v_{3}\) to the sink via \(v_{1}\) is \(E_{1}^{3}=[(2L_{3}-3)(1-OR_{1,3})+2]e=2.5e\), while that of selecting \(v_{4}\) as the gathering node of \(v_{3}\) is \(E_{4}^{3}=[(2L_{3}-1)(1-OR_{3,4})+2]e=2.9e\). Therefore, \(E_{4}^{3}>E_{1}^{3}\), which is consistent with above analysis. Case 2: \(OR_{i,k}<OR_{T}\) and \(OR_{j,k}\geq OR_{T}\). \(v_{k}\) chooses \(v_{j}\) as its gathering node, according to Rule 1. From Case 1 and Case 2, when \(v_{k}\) gets \(OR_{j,k}\geq OR_{T}\), \(v_{k}\) selects its gathering node from the candidate parent nodes, and does not need to calculate the overlapping rates of sensing area with its neighbor nodes. Figure 4: Gathering node selection for \(v_{3}\). Case 3: \(OR_{i,k}\geq OR_{T}\) and \(OR_{j,k}<OR_{T}\). Node \(v_{k}\) has two ways to send its data. One option is that \(v_{k}\) becomes an independent node while \(v_{j}\) is its relay node, and the total energy consumption of transmitting data of \(v_{k}\) to the sink via \(v_{j}\) is  
\[E_{j}^{k}=(2L_{k}-1)e. \tag{5}\]  
The other option is taking \(v_{i}\) as \(v_{k}\)'s gathering node, and the total energy cost is shown in Equation (3). Hence \(E_{i}^{k}-E_{j}^{k}=[2-(2L_{k}-1)(1-\alpha)]e\). If \((2L_{k}-1)OR_{j,k}>2\), then \(E_{i}^{k}<E_{j}^{k}\), and \(v_{k}\) chooses \(v_{i}\) as its gathering node. In one word, if there is no candidate parent node \(v_{j}\) subject to \(OR_{j,k}\geq OR_{T}\), a neighbor node \(v_{i}\) with \(OR_{i,k}\geq OR_{T}\) and \((2L_{k}-1)OR_{i,k}>2\) is selected as the gathering node of \(v_{k}\). Furthermore, if no such neighbor node exists, \(v_{k}\) becomes an independent node. Case 4: \(OR_{i,k}<OR_{T}\) and \(OR_{j,k}<OR_{T}\). Considering the weak similarity, it is not necessary to aggregate the data from these nodes. Therefore, \(v_{k}\) becomes an independent node, delivering its data to the sink without aggregation. In conclusion, for free nodes, their candidate parent nodes have high priorities to be the gathering nodes. If all the candidate parent nodes have lower overlapping rates of sensing area than the threshold, then the neighbor nodes are considered to aggregate data. **Rule 3. **_Data from every node is aggregated at most once, and in relay node selection, the non-gathering nodes take priorities over the candidate parent node with the most residual energy._  
Since data similarity is small between different gathering areas, data aggregation inter gathering areas probably has no significant advantages. Additionally, the data collection and processing for further aggregations may prolong the end-to-end delay. Consequently, in AggOR, taking into account the original data from each node, the aggregation executes at most once. Obviously, the gathering nodes consume more power than the member nodes and the independent nodes, and thus are not suitable as relay nodes which need to contribute extra energy for data forwarding. Selecting non-gathering nodes as relays helps to balance the energy consumption in the entire network and prolong the network lifetime. If no non-gathering node exists, take the candidate parent node with the most remaining energy as the forwarder.