For any fixed c ≥ 1, there exist finite metric spaces whose Vietoris-Rips filtration cannot be c-approximated by any finitely presented construction of linear size; for c < √2, exponential size is required.
Primoz Skraba and Katharine Turner
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
years
2026 2representative citing papers
Random slicing for subsampling combined with Nadaraya-Watson smoothing enables faster and improved persistence-based topological optimization of point clouds in 2D and 3D.
citing papers explorer
-
Lower Bounds for Approximating the Vietoris-Rips Filtration
For any fixed c ≥ 1, there exist finite metric spaces whose Vietoris-Rips filtration cannot be c-approximated by any finitely presented construction of linear size; for c < √2, exponential size is required.
-
Towards Scalable Persistence-Based Topological Optimization
Random slicing for subsampling combined with Nadaraya-Watson smoothing enables faster and improved persistence-based topological optimization of point clouds in 2D and 3D.