A Note on the Simplex-Tree Construction of the Vietoris-Rips Complex
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We give an alternative presentation of the Simplex Tree construction of the Vietoris-Rips complex <cit.>, which highlights how it takes advantage of a small amount of combinatorial structure in the k-skeleton of the complex in order to avoid unnecessary comparisons when identifying its (k+1)-simplices. We then show that it achieves an order-of-magnitude speedup over the Incremental-VR algorithm in Zomorodian <cit.> when constructing the clique complexes of Erdős-Rényi graphs.
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