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.

翻译：空间填充曲线（SFC）通过对多维空间进行网格划分并对网格单元施加线性序，将多维空间中的点映射为一维点。由此，SFC可利用B+树等一维索引结构实现多维数据的索引。选择恰当的SFC至关重要，因为不同SFC对查询性能影响各异。当前存在两种主要策略：1）确定性方案，计算高效但通常导致次优的查询性能；2）动态方案，基于代价函数考虑广泛的候选SFC集合，但会带来显著的计算开销。然而，现有方法在面对繁重查询工作负载和大量SFC选项时，无法有效度量SFC的效能。针对此问题，我们提出了常数时间代价估计方法，能够增强现有SFC选择算法，使其能学习更有效的SFC。此外，我们提出一种利用强化学习与所提代价估计方法高效选择SFC模式的学习方法。实验证据表明，所提出的代价估计与SFC学习方法兼具有效性与高效性。