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

Jean-Daniel Boissonnat 1, 2 Clément Maria 2, 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : This paper introduces a new 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 imple- ment 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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Submitted on : Friday, September 23, 2016 - 3:25:14 PM
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Jean-Daniel Boissonnat, Clément Maria. The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes. 20th Annual European Symposium, Ljubljana, Slovenia, September 10-12, 2012. Proceedings, Sep 2012, Ljubljana, Slovenia. pp.731-742, ⟨10.1007/978-3-642-33090-2_63⟩. ⟨hal-01108441⟩

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