A Survey of Learned Indexes for the Multi-dimensional Space

A recent research trend involves treating database index structures as Machine Learning (ML) models. In this domain, single or multiple ML models are trained to learn the mapping from keys to positions inside a data set. This class of indexes is known as "Learned Indexes." Learned indexes have demonstrated improved search performance and reduced space requirements for one-dimensional data. The concept of one-dimensional learned indexes has naturally been extended to multi-dimensional (e.g., spatial) data, leading to the development of "Learned Multi-dimensional Indexes". This survey focuses on learned multi-dimensional index structures. Specifically, it reviews the current state of this research area, explains the core concepts behind each proposed method, and classifies these methods based on several well-defined criteria. We present a taxonomy that classifies and categorizes each learned multi-dimensional index, and survey the existing literature on learned multi-dimensional indexes according to this taxonomy. Additionally, we present a timeline to illustrate the evolution of research on learned indexes. Finally, we highlight several open challenges and future research directions in this emerging and highly active field.

The "AI+R"-tree: An Instance-optimized R-tree

The emerging class of instance-optimized systems has shown potential to achieve high performance by specializing to a specific data and query workloads. Particularly, Machine Learning (ML) techniques have been applied successfully to build various instance-optimized components (e.g., learned indexes). This paper investigates to leverage ML techniques to enhance the performance of spatial indexes, particularly the R-tree, for a given data and query workloads. As the areas covered by the R-tree index nodes overlap in space, upon searching for a specific point in space, multiple paths from root to leaf may potentially be explored. In the worst case, the entire R-tree could be searched. In this paper, we define and use the overlap ratio to quantify the degree of extraneous leaf node accesses required by a range query. The goal is to enhance the query performance of a traditional R-tree for high-overlap range queries as they tend to incur long running-times. We introduce a new AI-tree that transforms the search operation of an R-tree into a multi-label classification task to exclude the extraneous leaf node accesses. Then, we augment a traditional R-tree to the AI-tree to form a hybrid "AI+R"-tree. The "AI+R"-tree can automatically differentiate between the high- and low-overlap queries using a learned model. Thus, the "AI+R"-tree processes high-overlap queries using the AI-tree, and the low-overlap queries using the R-tree. Experiments on real datasets demonstrate that the "AI+R"-tree can enhance the query performance over a traditional R-tree by up to 500%.