## 4 Experiments and Results
### Multiple Watermark Capacity  
The multiple watermark capacity, which indicates the number of watermarks embedded in the cover data, serves as a crucial indicator for evaluating the effectiveness of a multiple watermark algorithm. The authors of [36] present a multiple watermarking algorithm that exhibits good performance in terms of robustness for small datasets. Therefore, this algorithm is chosen for the comparative experiments detailed in this section. In [36], the watermarks are embedded into non-repetitive sets of the cover data, and one watermark bit is embedded into many vertices. This algorithm shows good performance in terms of watermark capacity.  
To maximize watermark embedding while ensuring algorithm robustness, it is essential to analyze the multiple watermark capacity of the proposed algorithm via specific experimental steps. In this study, we employed the proposed algorithm to embed watermarks into 10 vector geographic datasets containing numerous coordinate vertices. The maximum number of watermarks that can theoretically be embedded was calculated based on the size of each experimental dataset. The watermarks were embedded in the same 10 experimental maps using the program described in [36]. The embedding process continued until no additional watermarks could be inserted into the cover maps, and the number of embedded watermarks was simultaneously recorded. Subsequently, watermark extraction and detection were performed on the experimental data. The results of these experiments are presented in Table 12. Furthermore, the same program was repeated on 10 experimental vector geographic datasets containing a small number of coordinate vertices.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**No.** & **Data** & **Data** & **No.** & **Data** & **Data** & **No.** & **Data** & **Data** & **Data** & **Data** \\
2 & Point & 511 & 7 & Point & 2797 & 12 & Polyline & 3541 & 17 & Polygon & 2301 \\
3 & Point & 756 & 8 & Point & 3568 & 13 & Polyline & 4653 & 18 & Polygon & 3246 \\
4 & Point & 1158 & 9 & Point & 4972 & 14 & Polyline & 4977 & 19 & Polygon & 4983 \\
5 & Point & 1514 & 10 & Point & 5657 & 15 & Polyline & 5321 & 20 & Polygon & 5269 \\ \hline \hline \end{tabular}
\end{table}
Table 9: List of experimental maps.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{3}{*}{**Attacks**}} & \multicolumn{4}{c}{**Watermark 1**} & \multicolumn{4}{c}{**Detected Results**} \\ \cline{2-11}  & \multicolumn{2}{c}{**Attacks**} & \multicolumn{2}{c}{**Watermark 1**} & \multicolumn{2}{c}{**Watermark 2**} & \multicolumn{2}{c}{**Watermark 3**} & \multicolumn{2}{c}{**Watermark 4**} \\ \cline{3-11}  & \multicolumn{2}{c}{**Proposed**} & \multicolumn{2}{c}{**Reference [35]**} & \multicolumn{2}{c}{**Proposed**} & \multicolumn{2}{c}{**Reference [35]**} & \multicolumn{2}{c}{**Proposed**} & \multicolumn{2}{c}{**Reference [35]**} & \multicolumn{2}{c}{**Proposed**} & \multicolumn{2}{c}{**Reference [35]**} \\  & & **Algorithm** &  
Table 12 demonstrates that the proposed algorithm exhibits superior watermark capacity, which remains consistently high regardless of the data type or experimental volume. In contrast, the watermark capacity of the algorithm presented in [36] is significantly impacted by the data quantity. The watermark capacity increases with the increase in data size. The algorithm in [36] needs to randomly divide the coordinate vertices into non-overlapping datasets before embedding watermarks, so the number of embedded watermarks still depends on the total number of coordinate vertices. The number of watermarks that can be embedded simultaneously also escalates with the increase in the count of coordinate vertices. The proposed algorithm performs multiple quantization on a limited number of coordinate vertices, thus ensuring that the embedded watermark count remains unaffected by the number of coordinate vertices.