# Dual Clustering-Based Method for Geospatial Knowledge Graph Partitioning
## 3 Experiments
### Results
#### 3.3.2 Spatial-Graph Coupled Query Experimental Results  
For withinDistance-graph coupled queries, GKGP-DC exhibits significant performance improvements (Table 3, Figure 11). For a withinDistance-star query, the proposed algorithm reduces the query response time by at least 0.868 s and up to 2.102 s. For a withinDistance-snowflake query, the reduction is at least 4.786 s and up to 15.325 s. The proposed method has a significant improvement on a withinDistance-chain query and a withinDistance-complex query, whose response time is reduced by at least 9.098 s and up to 23.053 s and at least 10.429 s and up to 22.260 s, respectively.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **withinDistance–Star Query** & **withinDistance–Snowflake Query** & **withinDistance–Chain Query** & **withinDistance–Complex Query** \\ \hline hash & 5.739 & 26.248 & 36.128 & 38.154 \\ LDG & 5.821 & 23.245 & 35.759 & 38.047 \\ FENNEL & 4.587 & 24.056 & 34.802 & 37.095 \\ wstream & 5.407 & 22.108 & 33.252 & 37.165 \\ HeiStream & 5.424 & 21.236 & 33.285 & 37.043 \\ IHCGP & 5.705 & 19.094 & 32.908 & 37.094 \\ METIS & 5.043 & 16.246 & 22.571 & 26.981 \\ parmetis & 5.103 & 15.709 & 22.545 & 26.323 \\ KaFFPa & 5.152 & 15.745 & 22.173 & 26.584 \\ xtraPuLP & 4.648 & 15.879 & 22.556 & 26.427 \\ GKGP-DC & 3.719 & 10.923 & 13.075 & 15.894 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Response time of withinDistance–graph coupled query (unit: seconds).  
Figure 11: Response time of withinDistance–graph coupled query (unit: seconds).  
For buffer-graph coupled queries, the proposed algorithm also performs better compared to other partitioning methods (Table 4, Figure 12). Specifically, for a buffer-star query, the proposed algorithm reduces the query response time by at least 1.797 s and up to 2.487 s. For a buffer-snowflake query, the reduction is at least 4.907 s and up to 19.571 s. As for buffer-chain queries and buffer-complex queries, the response time is reduced by at least 7.162 s and up to 19.506 s and at least 10.756 s and up to 22.774 s, respectively.  
The result of a kNN-graph coupled query also shows that GKGP-DC outperforms the comparison methods (Table 5, Figure 13). For example, the proposed algorithm reduces the query response time by at least 0.586 s and up to 0.886 s on a kNN-star query. For a kNN-snowflake query, the reduction is at least 4.992 s and up to 12.360 s. For a kNN-chain query, the response time is reduced by at least 5.172 s and up to 13.258 s. And for a kNN-complex query, the response time is reduced by at least 4.248 s and up to 16.845 s.  
In addition, Table 6 and Figure 14 show that GKGP-DC exhibits significant performance improvements when handling different intersect-graph coupled queries. Specifically, for an intersect-star query, the proposed algorithm reduces the query response time by at least 0.472 s and up to 3.078 s. For an intersect-snowflake query, the reduction is at least 2.613 s and up to 10.772 s. For an intersect-chain query, the response time is reduced by at  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Buffer-Star Query** & **Buffer-Snowflake Query** & **Buffer-Chain Query** & **Buffer-Complex Query** \\ \hline hash & 4.045 & 28.699 & 32.367 & 35.879 \\ LDG & 4.630 & 24.158 & 29.410 & 33.543 \\ Fennel & 4.015 & 24.537 & 29.072 & 33.109 \\ wstream & 4.403 & 23.789 & 29.328 & 33.132 \\ Heisream & 4.352 & 21.585 & 29.091 & 33.096 \\ IHCGP & 4.705 & 20.956 & 27.923 & 30.745 \\ METIS & 4.043 & 15.114 & 21.518 & 24.511 \\ parmetis & 4.233 & 15.393 & 21.531 & 24.462 \\ KaFFPa & 4.192 & 14.035 & 20.023 & 23.861 \\ xtraPuLP & 4.048 & 14.752 & 21.479 & 24.533 \\ GKGP-DC & 2.218 & 9.128 & 12.861 & 13.105 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Response time of buffer–graph coupled query (unit: seconds).  
Figure 12: Response time of buffer–graph coupled query (unit: seconds).