Improved Approximate Rips Filtrations with Shifted Integer Lattices
نویسندگان
چکیده
Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a combinatorial explosion in the complex size. For n points in R, we present a scheme to construct a 3 √ 2approximation of the multi-scale filtration of the L∞-Rips complex, which extends to a O(d0.25)approximation of the Rips filtration for the Euclidean case. The k-skeleton of the resulting approximation has a total size of n2O(d log k). The scheme is based on the integer lattice and on the barycentric subdivision of the d-cube. 1998 ACM Subject Classification F.2.2 Geometrical problems and computations
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