# A Type of Low-Latency Data Gathering Method with Multi-Sink for Sensor Networks
## 4 Data Gathering with the Help of Multi-Sink
### Redundancy Reduction on Data Gathering
#### 4.2.2 Sensing Radius Adjustment  
It is known that the coverage redundancy of the network could decrease with the help of the active node selection method in Section 4.2.1. However, there are still some active nodes at the boundary of each DGA that could go into sleeping mode, as \(S_{S}\) and \(S_{9}\) shown in Figure 7. Besides, the length of sensing radius \(R_{S}(S_{i})\) calculated by Formula (8) may not be optimal. The redundant region may still exist between the adjacent sensing areas. Therefore, sensing radius of the active nodes should be further adjusted.  
For the grid whose coordinate meets the condition of Formulas (9) and (10), it is known that, it is not in the circle \(S_{i}\) whose radius is \(R_{S}(S_{i})-\Delta d\), as the gray girds shown in Figure 9. In this case, \(g_{j}=g_{j}-1\).  
\[\left(x_{j}\pm\frac{m}{2}-x\left(S_{i}\right)\right)^{2}+\left(y_{j}\pm\frac{ l}{2}-y\left(S_{i}\right)\right)^{2}>\left(R_{S}\left(S_{i}\right)-\Delta d\right)^{2} \tag{10}\]  
Figure 8: Overlapping sensing area judgment based on grids.  
In Formula (10), \(\Delta d\) is a constant and it should meet  
\[\Delta d>\sqrt{l^{2}+m^{2}} \tag{11}\]  
If there is no grid satisfying \(g_{j}=0\) in the annular region whose outer and inner radiuses are \(R_{S}(S_{i})\) and \(R_{S}(S_{i})-\Delta d\) respectively, we set \(R_{S}(S_{i})=R_{S}(S_{i})-\Delta d\). This judgement process repeats until one of the two following conditions exist:  
If there is at least one grid satisfying \(g_{i}=0\), the current value of \(R_{S}(S_{i})\) will be set as the sensing radius. Then, we have \(g_{j}=g_{j}+1\) for all the grids in the annular region.  
If the value of \(R_{S}(S_{i})\) is 0, it is known that the sensing area of \(S_{i}\) is completely covered by that of other active nodes (such as \(S_{S}\) and \(S_{9}\) shown in Figure 7). Then, \(S_{i}\) will go into sleeping mode.  
Nodes whose sensing areas are at the boundary of the DGAs adjust the length of their sensing radiuses firstly according to the above steps. For ease of description, it is defined that node which located at the sensing region of \(S_{i}\) and in the same DGA with it is the neighbor of \(S_{i}\). Thus, the number of neighbors (defined as \(Nei(S_{i})\)) of the node located at the boundary of DGA is often smaller than that of the node inside the DGA. Then we have,  
\[\Delta\rho\left(S_{i}\right)=n/M\times L-Nei\left(S_{i}\right)/\pi R_{S}\left( S_{i}\right)^{2} \tag{12}\]  
If and only if \(\Delta\rho(S_{i})\) is greater than a threshold \(\Delta\rho\), the sensing area of \(S_{i}\) exceeds the boundary of that DGA. In this case, \(S_{i}\) is called the \"boundary node\", just as \(S_{8}\), \(S_{9}\), \(S_{10}\) shown in Figure 7. The boundary nodes adjust the length of their sensing radiuses one by one according to the value of \(\Delta\rho(S_{i})\) (from high to low). It is obvious that the boundary node whose sensing areas are completely covered by other active nodes (including the nodes in other DGAs) goes into sleeping mode after this adjustment. Therefore, the redundancy of data gathered from the same DGA will be decreased.  
Subsequently, in each DGA the \"non-boundary nodes\" follow the same process. Moreover, to save energy as much as possible and to achieve balance of energy consumption, the node with the lower residual energy takes priority to do the sensing radius adjustment.