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arXiv · 2001.02581

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

Jean-Daniel Boissonnat·Clément Maria
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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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Jean-Daniel Boissonnat, Clément Maria. 2020-01-08. The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes. https://doi.org/10.1007/s00453-014-9887-3

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