LAZY R-tree: The R-tree with lazy splitting algorithm

Abstract

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.

Study on Spatio-Temporal Indexing Model of Geohazard Monitoring Data Based on Data Stream Clustering Algorithm

“…In recent years, a large number of spatial indexing techniques and methods have been proposed by domestic and foreign scholars and related researchers, with a wealth of spatial indexing techniques and methodologies emerging in recent times. Although a myriad of indexing techniques exist, the predominant dynamic spatial indexing structure in current use is the R-tree, as originally proposed by Guttman, along with its numerous variants [9][10][11][12][13][14][15][16]. These include the VoR-tree, as proposed by Mehdi Sharifzadeh, which effectively amalgamates Voronoi diagrams into the R-tree to enable efficient nearest-neighbor querying.…”

QRB-tree Indexing: Optimized Spatial Index Expanding upon the QR-tree Index

“…These indices divide the entire space into regions based on the approximate extent of the target features and later build a balance tree based on these regions. Due to the success of R-trees, many variants have been developed, including the R+-tree [16], R*-tree [17], Hilbert R-tree [18], priority R-tree (PR-tree) [19], R-tree with update memo (RUM-tree) [20], and LAZY R-tree [21]. Singh and Bawa [22] compared the R-tree variants.…”

High‐performance implementation of a two‐bit geohash coding technique for nearest neighbor search

“…NNS in R‐trees is accelerated by recursively searching each child of the current node whose bounding rectangle overlaps the query region 20,21 . An R‐tree with lazy splitting method and R+ trees are some of the improved versions of R‐tree that have attracted the focus of many researchers in this direction 22‐24 . The downside of these trees is the difficulty of constructing a balanced tree such that its rectangles do not cover too much empty space and do not overlap too much.…”