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arXiv:2001.02581cs.CG

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.

arXiv comments
Journal reference
Algorithmica, Springer Verlag, 2014, 70 (3), pp.20
DOI
doi:10.1007/s00453-014-9887-3
Subjects
cs.CGComputational Geometry

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  1. Show HN: Hypergraph, a data structure library to generate directed hypergraphs 1 comment

    • And for simplicial complexes there's a neat data structure: https://arxiv.org/abs/2001.02581 It's implemented (minus some features) in e.g. GUDHI.

      gsprView on HNParent context

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