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.
Improved approximate Rips filtrations with shifted integer lattices and cubical com- plexes.Journal of Applied and Computational Topology, 5(3):425–458, 2021
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.AT 1years
2026 1verdicts
ACCEPT 1representative citing papers
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.