Reinforcement learning has recently been used to enhance index structures, giving rise to reinforcement learning-enhanced spatial indices (RLESIs) that aim to improve query efficiency during index construction. However, their practical benefits remain unclear due to the lack of unified implementations and comprehensive evaluations, especially in disk-based settings. We present the first modular and extensible benchmark for RLESIs. Built on top of an existing spatial index library, our framework decouples index training from building, supports parameter tuning, and enables consistent comparison with traditional, advanced, and learned spatial indices. We evaluate 12 representative spatial indices across six datasets and diverse workloads, including point, range, kNN, spatial join, and mixed read/write queries. Using latency, I/O, and index statistics as metrics, we find that while RLESIs can reduce query latency with tuning, they consistently underperform learned spatial indices and advanced variants in both query efficiency and index build cost. These findings highlight that although RLESIs offer promising architectural compatibility, their high tuning costs and limited generalization hinder practical adoption.

Cardinality estimation (CE), the task of predicting the result size of queries is a critical component of query optimization. Accurate estimates are essential for generating efficient query execution plans. Recently, machine learning techniques have been applied to CE, broadly categorized into query-driven and data-driven approaches. Data-driven methods learn the joint distribution of data, while query-driven methods construct regression models that map query features to cardinalities. Ideally, a CE technique should strike a balance among three key factors: accuracy, efficiency, and memory footprint. However, existing state-of-the-art models often fail to achieve this balance. To address this, we propose CoLSE, a hybrid learned approach for single-table cardinality estimation. CoLSE directly models the joint probability over queried intervals using a novel algorithm based on copula theory and integrates a lightweight neural network to correct residual estimation errors. Experimental results show that CoLSE achieves a favorable trade-off among accuracy, training time, inference latency, and model size, outperforming existing state-of-the-art methods.

A space-filling curve (SFC) maps points in a multi-dimensional space to one-dimensional points by discretizing the multi-dimensional space into cells and imposing a linear order on the cells. This way, an SFC enables computing a one-dimensional layout for multidimensional data storage and retrieval. Choosing an appropriate SFC is crucial, as different SFCs have different effects on query performance. Currently, there are two primary strategies: 1) deterministic schemes, which are computationally efficient but often yield suboptimal query performance, and 2) dynamic schemes, which consider a broad range of candidate SFCs based on cost functions but incur significant computational overhead. Despite these strategies, existing methods cannot efficiently measure the effectiveness of SFCs under heavy query workloads and numerous SFC options. To address this problem, we propose means of constant-time cost estimations that can enhance existing SFC selection algorithms, enabling them to learn more effective SFCs. Additionally, we propose an SFC learning method that leverages reinforcement learning and our cost estimations to choose an SFC pattern efficiently. Experimental studies offer evidence of the effectiveness and efficiency of the proposed means of cost estimation and SFC learning.

Learned indices can leverage the high prediction accuracy and efficiency of modern deep learning techniques. They are capable of delivering better query performance than traditional indices over one-dimensional data. Recent studies demonstrate that we can also achieve query-efficient learned in-dices for spatial data by partitioning and subsequently transforming spatial data to one-dimensional values, after which existing techniques can be applied. While enabling efficient querying, building and rebuilding learned spatial indices efficiently remains largely unaddressed. As the model training needed to learn a spatial index is costly, efficient building and rebuilding of learned spatial indices on large data sets is challenging if performed by means of model training and retraining.To advance the practicality of learned spatial indices, we propose a system named ELSI that enables the efficient building and rebuilding of a class of learned spatial indices that follow two simple design principles. The core idea is to reduce the model (re-)building times by engineering reduced training sets that preserve key data distribution patterns. ELSI encompasses a suite of methods for constructing small and distribution-preserving training sets from input data sets. Further, given an input data set, ELSI can adaptively select a method that produces a learned index with high query efficiency. Experiments on real data sets of 100+ million points show that ELSI can reduce the build times of four different learned spatial indices consistently (by up to two orders of magnitude) without jeopardizing query efficiency.

We study result diversification in continuous spatial query processing and formulate a new type of queries, the moving k diversified nearest neighbor query (MkDNN). Given a moving query object, an MkDNN query maintains continuously the k diversified nearest neighbors of the query object. Here, how diversified the nearest neighbors are is defined on the distance between the nearest neighbors. We propose an algorithm to maintain incrementally the k diversified nearest neighbors to reduce the costs of continuous query processing. We further propose two approximate algorithms to obtain even higher query efficiency with precision bounds. We verify the effectiveness and efficiency of the proposed algorithms empirically. The results confirm the superiority of the proposed algorithms.

As a major type of continuous spatial queries, the moving$k$nearest neighbor ($k$NN) query has been studied extensively. However, most existing studies have focused on only the query efficiency. In this paper, we consider further the usability of the query results, in particular the diversification of the returned data points. We thereby formulate a new type of query named themoving$k$diversified nearest neighbor query (M$k$DNN). This type of query continuously reports the$k$diversified nearest neighbors while the query object is moving. Here, the degree of diversity of the$k$NN set is defined on the distance between the objects in the$k$NN set. Computing the$k$diversified nearest neighbors is an NP-hard problem. We propose an algorithm to maintain incrementally the$k$diversified nearest neighbors to reduce the query processing costs. We further propose two approximate algorithms to obtain even higher query efficiency with precision bounds. We verify the effectiveness and efficiency of the proposed algorithms both theoretically and empirically. The results confirm the superiority of the proposed algorithms over the baseline algorithm.