## 4 Cluster Sleep-Wake Scheduling Algorithm
### Related Work
#### Handling Boundary Nodes  
**Definition 12** (Boundary region).: _A region consisting of all partition units which \(j=1\) or \(k=\lceil\frac{\sqrt{22}m}{r_{c}}\rceil\)._  
Of these, \(m\) represents the height of the monitoring area. As shown in Figure 11.  
**Definition 13** (Boundary node).: _All sensor nodes are located in the boundary area._  
In an ocean monitoring network, due to the influence of tides, nodes deployed in the water must not be stationary. We must therefore consider the effect of the node's movement on coverage. Because node movement does not produce a change in relative position, the coverage does not shift  
Figure 11: Boundary region.  
considerably; for most nodes, it is unnecessary to consider the effect of node movement on coverage. However, nodes at the boundary, including those at the left boundary and the upper boundary, must consider the impact of node movement on coverage. A specific sensing radius must thus be designed. A high coverage rate can be achieved even if the node leaves the partition unit.  
Assuming that the node is in a relatively stable ocean environment, the node will be thrust by the wave to the right, so the node only changes the coordinates on the \(x\)-axis and the \(z\)-axis during the motion. Since the nodes are pulled by the ropes, they do not move with the seawater to a distant distance position, but move within a certain range. As shown in Figure 12, it is the force of the node under water. According to this, the movement of the underwater node is a cyclical process. Therefore, the node moves along the curve from point A to point B, and then accelerates and then decelerates until the speed is zero. Randomly take a time \(T_{p}\) in the time range \([T_{min},T_{max}]\) to describe the time when the node remains stationary at point B. Then use point B as the starting point to do the above movement. This cycle is the process of the node moving underwater. Because of the border node moves, there are coverage holes in the border area of the monitoring area. To solve this problem, it is necessary to reset the sensing radius of the boundary node.  
It is assumed that the sensor node can obtain its own position coordinates according to the positioning algorithm under water. The coordinates of the node at the A position are \((x_{1},y_{1},z_{1})\), and the coordinates of the node at the B position are \((x_{2},y_{1},z_{2})\), as shown in Figure 12. Therefore, it can be known that when the moving speed of the node is zero, the horizontal distance \((d_{0})\) and the vertical distance \((h_{0})\) from the initial position are respectively.  
\[d_{0}=x_{2}-x_{1} \tag{16}\]  
\[h_{0}=z_{2}-z_{1} \tag{17}\]  
Therefore, when the node is located in the partition unit of \(j=1\), the perceived radius of the node is set to:  
\[r_{s}=r_{s}+d_{0} \tag{18}\]  
When the node is located in the partition unit of \(k=\lceil\frac{\sqrt{2}m}{r_{c}}\rceil\), the perceived radius of the node is set to:  
Figure 12: Stress and motion of nodes under water.  
\[r_{s}=r_{s}+h_{0} \tag{19}\]  
where \(r_{c}\) represents the communication radius of the sensor node and \(m\) represents the water depth of the monitored water.  
In addition, when \(j=1\) and \(k=\lceil\frac{\sqrt{22}m}{r_{c}}\rceil\), compare the size of \(h_{0}\) and \(d_{0}\), if \(h_{0}>d_{0}\), the node sensing radius is set to:  
\[r_{s}=r_{s}+h_{0} \tag{20}\]  
Conversely, the node's sensing radius is set to:  
\[r_{s}=r_{s}+d_{0} \tag{21}\]