Fig. 1.

Hausdorff distances and runtimes for various Hopper and Treehopper routines, with Geometric Sketching for comparison, on ∼1.3 million mouse neurons (a, b) and ∼2 million developing organ cells (c, d). For the Treehopper tests, the number of partitions d is indicated parenthetically in the legends. The basic Hopper routine produces the lowest Hausdorff distance obtainable in polynomial time, with our faster Treehopper routines nearly realizing the optimum. All significantly outperform Geometric Sketching, and show more consistent Hausdorff performance. Both Hopper and Treehopper take time linear in the sketch size, with slope depending on the overall dataset size and the degree of pre-partitioning. Geometric Sketching performs variably depending on the dataset’s geometry