English

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}
}
R2 v1 2026-06-23T13:06:04.662Z