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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 the indexing of multi-dimensional data using a one-dimensional index such as a B+-tree. 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 estimation 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 using neural networks have been shown to outperform traditional indices such as B-trees in both query time and memory. However, learning the distribution of a large dataset can be expensive, and updating learned indices is difficult, thus hindering their usage in practical applications. In this paper, we address the efficiency and update issues of learned indices through agile model reuse. We pre-train learned indices over a set of synthetic (rather than real) datasets and propose a novel approach to reuse these pre-trained models for a new (real) dataset. The synthetic datasets are created to cover a large range of different distributions. Given a new dataset DT, we select the learned index of a synthetic dataset similar to DT, to index DT. We show a bound over the indexing error when a pre-trained index is selected. We further show how our techniques can handle data updates and bound the resultant indexing errors. Experimental results on synthetic and real datasets confirm the effectiveness and efficiency of our proposed lazy (model reuse) approach.