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The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes

Jean-Daniel Boissonnat 1 Clément Maria 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the complex. This data structure allows to efficiently implement a large range of basic operations on simplicial complexes. We provide theoretical complexity analysis as well as detailed experimental results. We more specifically study Rips and witness complexes.
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https://hal.inria.fr/hal-00707901
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Submitted on : Monday, January 6, 2020 - 6:35:20 PM
Last modification on : Friday, January 21, 2022 - 4:10:03 AM
Long-term archiving on: : Wednesday, April 8, 2020 - 12:40:43 AM

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Jean-Daniel Boissonnat, Clément Maria. The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes. Algorithmica, Springer Verlag, 2014, 70 (3), pp.20. ⟨10.1007/s00453-014-9887-3⟩. ⟨hal-00707901v3⟩

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