The spatial index is a data structure formed according to the position and shape of the spatial object or the relationship between the spatial objects according to certain rules, and the spatial data is managed by an effective spatial data structure. The quality of a spatial index directly affects the performance of spatial queries. The R-tree index structure is a highly efficient spatial index. According to the R-tree query rule, when performing spatial query, most data that is not related to the query condition can be filtered out, and finally, a few leaf nodes can be accessed to query the data satisfying the condition. Its query performance is affected by factors such as non-leaf node overlap and node space utilisation. This article proposes a lazy splitting method to improve the R-tree construction process. The scheme works as follows: (1) When a node overflows, it creates an overflow node for that node and all overflow nodes are saved in a hash table. (2) If the node continues to insert data, the data are added to its overflow node. (3) When an overflow node is saturated, the node and its overflow node are split into two saturated nodes. We use both simulated and actual data to perform experiments. The experimental results show that an R-tree constructed by the lazy algorithm is superior to an R-tree constructed using the original R-tree PM algorithm or the corner-based splitting (CBS) algorithm based on the number of splits created, the node space used and the efficiency of region queries and k-nearest neighbour (kNN) queries.

中文翻译：

---

LAZY R-tree：具有惰性分裂算法的 R 树

空间索引是根据空间对象的位置、形状或空间对象之间的关系，按照一定的规则形成的数据结构，空间数据由有效的空间数据结构进行管理。空间索引的质量直接影响空间查询的性能。R-tree索引结构是一种高效的空间索引。根据R-tree查询规则，在进行空间查询时，可以过滤掉大部分与查询条件无关的数据，最后访问少数叶节点，查询满足条件的数据。其查询性能受非叶节点重叠和节点空间利用率等因素影响。本文提出了一种惰性分裂方法来改进R树的构建过程。该方案的工作原理如下：(1) 当一个节点溢出时，为该节点创建一个溢出节点，所有溢出节点都保存在一个哈希表中。(2)如果节点继续插入数据，则将数据添加到其溢出节点。(3) 当一个溢出节点饱和时，该节点及其溢出节点被分裂成两个饱和节点。我们使用模拟数据和实际数据进行实验。实验结果表明，惰性算法构建的R树优于使用原始R树PM算法或基于角的分裂（CBS）算法构建的R树，基于创建的分裂数量，节点使用的空间以及区域查询和 k-最近邻 (kNN) 查询的效率。数据被添加到其溢出节点。(3) 当一个溢出节点饱和时，该节点及其溢出节点被分裂成两个饱和节点。我们使用模拟数据和实际数据进行实验。实验结果表明，惰性算法构建的R树优于使用原始R树PM算法或基于角的分裂（CBS）算法构建的R树，基于创建的分裂数量，节点使用的空间以及区域查询和 k-最近邻 (kNN) 查询的效率。数据被添加到其溢出节点。(3) 当一个溢出节点饱和时，该节点及其溢出节点被分裂成两个饱和节点。我们使用模拟数据和实际数据进行实验。实验结果表明，惰性算法构建的R树优于使用原始R树PM算法或基于角的分裂（CBS）算法构建的R树，基于创建的分裂数量，节点使用的空间以及区域查询和 k-最近邻 (kNN) 查询的效率。