# Efficient Top-\(k\) Spatial Dataset Search Processing
## 6 The Optimized Search Scheme
### The Optimized Search Algorithm
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Notations** & **Meanings** & **Parameter Values** \\ \hline \(\sigma\) & The similarity regulator & (0, 0.2, 0.5, 0.8, 1) \\ \(k\) & The number of requested spatial datasets & (5, 10, 15, 20, 25) \\ \(n\) & The number of spatial datasets & (2, 4, 6, 8, 10) \(\times\) 104 \\ \(u\) & The space-dividing threshold & (11, 12, 13, 14, 15) \\ \(\epsilon\) & The pooling threshold & (0, 1, 2, 3, 4,..., 12, 13) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter settings. exemplar dataset, with a smaller MSE indicating closer proximity between the two sets of points. Since \(\epsilon\) is solely used to accelerate the search and does not affect the search results, experiments evaluating search effectiveness do not include the parameter \(a\). Figures 5-9 illustrate the MSE of KSDS, KSDS+ and EMD as the parameters \(c\), \(\sigma\), \(k\), \(n\) and \(u\) vary. Figure 5 compares MSE versus \(c\) for the KSDS, KSDS+ and EMD algorithms. The parameter \(c\) denotes the number of cluster centers used in clustering the search results. An increase in \(c\) implies a larger number of cluster centers, resulting in the dataset being partitioned into more categories. As \(c\) increases, the MSE values for KSDS, KSDS+ and EMD all decrease. This decrease occurs because a higher number of cluster centers reduces the average distance between the search result points and their nearest cluster center. Figure 6 compares MSE versus \(\sigma\) for the KSDS, KSDS+ and EMD algorithms. The parameter \(\sigma\) serves as the similarity regulator in the similarity-calculation process. As the parameter \(\sigma\) decreases, the similarity calculation increasingly emphasizes quantitative similarity. Consequently, certain points outside the intersection of MCGs may contribute to a reduction in the average distance between location points within the datasets, thereby decreasing the overall MSE. Figure 7 compares MSE versus \(k\) for the KSDS, KSDS+ and EMD algorithms. The parameter \(k\) denotes the number of requested spatial datasets. As \(k\) increases, the MSE of KSDS, KSDS+ and EMD algorithms also increase. This is because a larger \(k\) results in the inclusion of more datasets with lower similarity in the search results, thereby leading to higher MSE values. Figure 5: MSE versus \(c\). Figure 6: MSE versus \(\sigma\). Figure 8 compares MSE versus \(n\) for the KSDS, KSDS+ and EMD algorithms. The parameter \(n\) denotes the number of spatial datasets. As \(n\) increases, the MSE values of algorithm KSDS, KSDS+ and EMD all decrease. This occurs because a larger number of datasets in the data repository enhances the likelihood of finding more similar results, thereby decreasing the MSE. Figure 9 compares MSE versus \(u\) for the KSDS, KSDS+ and EMD algorithms. The parameter \(u\) denotes the space-dividing threshold used in the grid partitioning process. The parameter \(u\) directly determines the number of grids within each dataset's MCG, thereby affecting the computational time overhead for each similarity calculation. As illustrated in the figure, a larger \(u\) results in increased search time cost. From Figures 5-9, it can be observed that KSDS and KSDS+ exhibit the same MSE. This is because KSDS+ primarily functions as a filtering mechanism, eliminating datasets that

Figure 8: MSE versus \(n\). Figure 7: MSE versus \(k\). Figure 9: MSE versus \(u\). are unlikely to be part of the final search result, without affecting the accuracy compared to KSDS. Additionally, the results demonstrate that both KSDS and KSDS+ achieve consistently lower MSE values compared to EMD. This indicates that our proposed methods are more effective in maintaining accuracy while optimizing the top-\(k\) search process, further validating their advantages. ### Search Efficiency Evaluation

This subsection evaluates the effectiveness of KSDS, KSDS-GMBR, KSDS-Pooling, KSDS+ and EMD for performing spatial dataset searches.