1. https://arxiv.org/abs/1506.08903
Table 2: VR = Vietoris Rips, W = weak witness, Wn = parametrized witness,
WRCF = weight rank clique filtration, and a = the alpha complex.

4. https://github.com/Ripser/ripser

8. https://arxiv.org/abs/1506.08903
Table 2: VR = Vietoris Rips, W = weak witness, Wn = parametrized witness,
WRCF = weight rank clique filtration, and a = the alpha complex.

12. https://arxiv.org/abs/1506.08903

13. comptop.stanford.edu/preprints/witness.pdf

14. http://web. cse. ohio-state

15. > δ ≤ δ D ⊆ V is a δ-net of V if
(i)  v ∈ V ,  d ∈ D such that ||v − d|| ≤ δ; and
(ii) no two points in D are within δ distance.
> δ
≤ δ

16. Choosing a δ-net :
Maxmin
1.) choose point l1 randomly
2.) If {l1, …, lk-1} have been chosen, choose lk such that {l1, …, lk-1} is in D - {l1, …, lk-1} and
min {d(lk, l1), …, d(lk, lk-1)} ≥ min {d(v, l1), …, d(v, lk-1)}