  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.
