Comparisons of the computational costs of pair-counting routines based on different data structures for periodic uniform random samples with different numbers of points in a cubic volume (left) and for sections between R_in and R_out of the same catalogues with respect to a corner of the boxes, where R_out is equal to the box size (right). The middle and bottom panels show results normalised by the costs with the k-d tree and kN², respectively. Here, the value of k is chosen such that the normalised costs at N = 5 × 10⁷ are unity.