## 3 Methodology
### Spatial Layer Construction
#### 3.1.2 Trie Tree for Managing Non-Equal Length-Encoding Sets
Since spatiotemporal data have inconsistent dimensional dimensions, using the time dimension as the third dimension makes its distribution more difficult to learn and the model construction more complicated. GLMI uses a spatiotemporal separation strategy to fully learn the distribution characteristics of spatiotemporal data, thereby accelerating queries. GLMI designs buffers and asynchronous merge strategies to solve the problem of difficult updates in existing learned indexes. ## 6 Conclusions

Compared with traditional indexes, learned indexes effectively reduce storage space and improve query efficiency by learning data distribution through machine learning models. Due to the large volume and uneven distribution of spatiotemporal data, their distribution is difficult to learn, which makes it difficult to build an efficient learned index. This paper adopts a time-space separation strategy, considers the different characteristics of spatial and temporal dimensions, and constructs a double-layer index. The spatial layer effectively solves the problem of uneven distribution of spatial data through Geohash-Hilbert dynamic partition encoding, ensures the robustness of the index structure in the face of skewed data, and ensures good spatial proximity. In the temporal layer, GLMI uses a piecewise linear model for data fitting to achieve the mapping of data keys to storage locations, further improving the query efficiency of the index. Experiments have shown that GLMI has obvious advantages over traditional indexes and the ZM index in storage space, query time, and insertion efficiency. In future work, we aim to extend GLMI's capabilities to handle dynamic operations such as updates and deletions more efficiently. We intend to explore the integration of spatiotemporal K-nearest neighbor (KNN) queries, which will further improve spatiotemporal data analysis capabilities. In addition, we plan to use the number of CPU operations as a key indicator for evaluating index performance, together with traditional indicators such as query efficiency and space consumption, to conduct a more comprehensive evaluation of computational cost. Conceptualization, K.C. and G.L. ; methodology, K.C. and G.C; software, K.C. ; validation, K.C., G.L., G.C., Z.W. and Q.C. ; formal analysis, G.L. and G.C; investigation, G.L. ; resources, G.L., Z.W. and Q.C. ; data curation, K.C. ; writing--original draft preparation, K.C. ; writing--review and editing, G.L. and G.C; visualization, K.C. and G.C. ; supervision, G.L., Z.W. and Q.C. ;project administration, K.C. ; funding acquisition, G.L. All authors have read and agreed to the published version of the manuscript. The project was supported by the Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation, Ministry of Natural Resources (KF-2023-08-25) and the National Natural Science Foundation of China (42372345). The data used in this experiment can be accessed through the URL [[https://www.nyc.gov/site/tlc/about/tlc-trip-record-data.page](https://www.nyc.gov/site/tlc/about/tlc-trip-record-data.page)]([https://www.nyc.gov/site/tlc/about/tlc-trip-record-data.page](https://www.nyc.gov/site/tlc/about/tlc-trip-record-data.page)) and [[https://www.microsoft.com/en-us/research/publication/t-drive-trajectory-data-sample/](https://www.microsoft.com/en-us/research/publication/t-drive-trajectory-data-sample/)]([https://www.microsoft.com/en-us/research/publication/t-drive-trajectory-data-sample/](https://www.microsoft.com/en-us/research/publication/t-drive-trajectory-data-sample/)), accessed on 18 October 2024. The authors declare no conflicts of interest. ## References

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