## 4 DHD-MEPO Algorithm
### Regional Unitization of the Network  
There are \(N\) mobile sensor nodes and static sensor nodes thrown in the target region, and the quantity of nodes is sufficient. The BS center is responsible for receiving all  
Figure 2: General flowchart of the DHD-MEPO algorithm. the data and centralizing the data transmitted by the nodes in turn. That results in an excessive load on the BS, and each node that carries the transmitted data may cause network congestion and consume more energy on the way to its destination. Therefore, to facilitate the management of the network region and save unnecessary energy consumption, the monitoring region is first divided into cells based on the quantity of randomly thrown nodes and the sensing area of the nodes, with each cell representing a unique ID number:  
\[V=\frac{4}{3}\pi R_{s}^{3}, \tag{7}\]  
\[\lceil N_{ideal}\rceil=\frac{k^{3}}{V}, \tag{8}\]  
\[D_{ratio}=\frac{\lceil N_{ideal}\rceil}{N}, \tag{9}\]  
\[M= \begin{cases}1,&0.9<D_{ratio}\leq 1\\ 2^{3},0.8<D_{ratio}\leq 0.9\\ 3^{3},0.7<D_{ratio}\leq 0.8^{\prime}\\ \ldots&\ldots\\ \end{cases}  \tag{10}\]  
\[c=\frac{k}{3\sqrt[3]{M}}, \tag{11}\]  
where \(V\) is the sensing area of a sensor node; \(N_{ideal}\) is the optimal quantity of nodes to be thrown in the region under ideal conditions, rounded upwards. \(D_{ratio}\) is the ratio of ideal to actual quantity of nodes thrown, the smaller the ratio, the more nodes the network actually deploys and the greater the number of cells to be divided. \(M\) is the total quantity of cells to be divided in the target region, the set is \(\mathrm{Q}=\{q_{1},q_{2},\ldots,q_{l},\ldots,q_{M}\}\), and \(c\) is the edge length of each cell divided. Figure 3 shows a diagram of the target region partitioned into cells according to different node densities. When the target region is divided into cells based on the density of nodes deployed, a group node is selected in each of the divided cells. The group node is responsible for further data fusion processing of the data received by the group before forwarding it to the BS. That minimizes energy consumption and simplifies network management by processing the information transmitted by the relevant nodes in groups. Load balancing is achieved to leng  
Figure 3: Cell division in the target region: (**a**) Area partitioned into \(3^{3}\) cells; (**b**) Area partitioned into \(4^{3}\) cells. Suppose that the quantity of cell bodies divided is 64 according to Equation (10), as shown in Figure 4a, and any one of its layers is taken for observation. Because of the initial throw of nodes at random, the quantity of nodes within each cell body is uneven. When too many nodes are distributed within a cell body, for example, in Figure 4b, cell body \(D_{(2,1,2)}\) is distributed with 10 nodes. If only one group node is selected within this cell body, it will lead to the group node carrying too much data information volume and quickly exhausting the energy of the group node, so at least two or more group nodes can be set up within this cell to jointly process the data information of the group. When too few nodes are distributed within a cell, e.g., cell \(D_{(4,1,4)}\) has only one node distributed, it would waste the resources of the node if the task of sending and receiving information to the BS is carried out alone. So, merge with neighbor cell bodies that remain connected and select an optimal node as a group node to aggregate data information. A boundary threshold is set and if the quantity of nodes within the cell is less than the lower limit of minimum threshold, it is merged with the surrounding neighbor cells. If the quantity of nodes within the cell exceeds the upper limit of the maximum threshold, more than two group nodes within the cell will be selected to be responsible for collecting information.