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.
Universality of the homotopy interleaving distance
3 Pith papers cite this work, alongside 37 external citations. Polarity classification is still indexing.
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Pith papers citing it
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representative citing papers
A pseudodistance on homotopy classes of maps is defined using interleavings of their extended tame persistence CDGA models derived from relative Sullivan algebras.
Presents ILP formulations to bound the interleaving distance on mapper graphs, with evaluation on small examples and benchmark datasets.
citing papers explorer
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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.
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A distance between maps via interleavings of relative Sullivan algebras
A pseudodistance on homotopy classes of maps is defined using interleavings of their extended tame persistence CDGA models derived from relative Sullivan algebras.
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Towards an Optimal Bound for the Interleaving Distance on Mapper Graphs
Presents ILP formulations to bound the interleaving distance on mapper graphs, with evaluation on small examples and benchmark datasets.