# An Efficient GNSS Coordinate Recognition Algorithm for Epidemic Management
## 6 Simulation Result
### Candidate Points and Outer Points  
The number of candidate points \(n_{\text{cand}}\) and the number of outer points \(n_{\text{outer}}\) are discussed in the following. Table 5 provides the values of \(n_{\text{cand}}\) for each algorithm used in the comparison. When the radius went from 1/16 to 1/256, \(n_{\text{cand}}\) of c_max went from 179,853 to 109,639, \(n_{\text{cand}}\) of c_min went from 148,369 to 108,609, and \(n_{\text{cand}}\) of c_avg went from about 162,264 to 109,121. With the same radius, \(n_{\text{cand}}\) of sqr went from 123,374 to 89,841, which was less than the values for c_max, c_min, and c_avg. In c_max, when the radius is 1/16, \(n_{\text{cand}}\) was 179,853 with a value of \(n_{inner}\) of 89,209, and the ratio of \(n_{\text{cand}}\) to \(n_{\text{inner}}\) was about 2.02. When the radius was from 1/16 to 1/256, the ratio of c_max ranged from about 2.02 to 1.23, the ratio of c_min went from about 1.67 to 1.22, and the ratio of c_avg went from about 1.82 to 1.22. Based on the same radius, the ratio of sqr went from 1.38 to 1.01, which was less than the values for c_max, c_min, and c_avg.  
Table 6 provides the number of outer points \(n_{\text{outer}}\). When the radius was 1/16, \(n_{\text{outer}}\) of c_max was 90,644, i.e., \(n_{\text{cand}}\) \(-\)\(n_{\text{inner}}\). When the radius went from 1/16 to 1/256, \(n_{\text{outer}}\) of c_max went from 90,644 to 20,430, \(n_{\text{outer}}\) of c_min went from 59,160 to 19,400, \(n_{\text{outer}}\) of c_avg went from about 73,055 to 19,912, and \(n_{\text{outer}}\) of sqr went from 34,165 to 632. When the radius was 1/16, \(n_{\text{outer}}\) of c_max was 90,644, and \(n_{\text{outer}}\) of sqr was 34,165. The number of outer points was reduced to 56,479, and the reduction rate was about 62.3% (=56,479/90,644). Figure 12 provides the reduction rates of c_max#sqr, c_min#sqr, and c_avg#sqr. When the radius was 1/16, the reduction rates of c_max#sqr, c_min#sqr, and c_avg#sqr were about 62.3%, 25.6%, and 53.2%. When the radius was reduced to 1/256, the reduction rates of c_max#sqr, c_min#sqr, and c_avg#sqr were about 96.9%, 91.9%, and 96.8%. Accordingly, sqr resulted in a reduction rate of the outer points between 25.6% and 96.9% with respect to c_max, c_min, and c_avg.  
Figure 11: The subarea reduction rates.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Radius**} & \multicolumn{2}{c}{**c\_max**} & \multicolumn{2}{c}{**c\_min**} & \multicolumn{2}{c}{**c\_avg**} & \multicolumn{2}{c}{**Sqr**} \\ \cline{2-9}  & \(n_{\text{cand}}\) & **Rate** & \(n_{\text{cand}}\) & **Rate** & \(n_{\text{cand}}\) & **Rate** & \(n_{\text{cand}}\) & **Rate** \\ \hline
1/16 & 179,853 & 2.02 & 148,369 & 1.66 & 162,264 & 1.82 & 123,374 & 1.38 \\ \hline
1/32 & 144,919 & 1.62 & 122,179 & 1.37 & 134,579 & 1.51 & 102,322 & 1.15 \\ \hline
1/64 & 121,457 & 1.36 & 115,708 & 1.30 & 119,440 & 1.34 & 93,721 & 1.05 \\ \hline
1/128 & 113,037 & 1.27 & 110,719 & 1.24 & 111,776 & 1.25 & 91,204 & 1.02 \\ \hline
1/256 & 109,639 & 1.23 & 108,609 & 1.22 & 109,121 & 1.22 & 89,841 & 1.01 \\ \hline \hline \end{tabular} The rate is \(n_{\text{cand}}\) divided by \(n_{\text{inner}}\).  
\end{table}
Table 5: The number of candidate points.