The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes
Computational Geometry
2020-01-09 v1
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.
Keywords
Cite
@article{arxiv.2001.02581,
title = {The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes},
author = {Jean-Daniel Boissonnat and Clément Maria},
journal= {arXiv preprint arXiv:2001.02581},
year = {2020}
}