get_levelset_components is O(n²) via pairwise is_face checks in computereeb

get_levelset_components(L) in cereeberus/compute/computereeb.py decides which simplices in the current sweep level-set belong to the same connected component by comparing every pair of simplices with is_face, which allocates two new set() objects per comparison:
for i, simplex1 in enumerate(L): for j, simplex2 in enumerate(L): if i < j: if is_face(simplex1, simplex2) or is_face(simplex2, simplex1): UF.union(i, j)

computeReeb calls this twice per sweep level, and the level-set can grow to hold a large fraction of the mesh's simplices, so this is a real cost driver for reasonably sized meshes. Confirmed directly against the current implementation: runtime roughly quadruples every time input size doubles (e.g. ~0.01s → ~11s from n=200 to n=6400).

Proposed fix

Since is_face(sigma, tau) just checks whether tau's vertex set is a subset of sigma's, each simplex's proper subsets (of every size, not just size 1 and 2) can be looked up directly in a dict keyed by tuple(sorted(subset)), instead of comparing every pair. A k-vertex simplex has 2^k - 2 nonempty proper subsets (6 for a triangle, 14 for a tetrahedron), so this is O(n·2^k) instead of O(n²) and stays cheap for any mesh with bounded simplex dimension

Profiled and proposed a fix here:

levelset_components_On2.ipynb