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- W2149966324 abstract "The (Vietoris-)Rips complex of a discrete point-set P is an abstract simplicial complex in which a subset of P defines a simplex if and only if the diameter of that subset is at most 1. We describe an efficient algorithm to determine whether a given cycle in a planar Rips complex is contractible. Our algorithm requires O(m log n) time to preprocess a set of n points in the plane in which m pairs have distance at most 1; after preprocessing, deciding whether a cycle of k Rips edges is contractible requires O(k) time. We also describe an algorithm to compute the shortest non-contractible cycle in a planar Rips complex in O(n2log n + mn) time." @default.
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- W2149966324 date "2008-06-09" @default.
- W2149966324 modified "2023-09-23" @default.
- W2149966324 title "Testing contractibility in planar rips complexes" @default.
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- W2149966324 doi "https://doi.org/10.1145/1377676.1377721" @default.
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