, Volume 70, Issue 3, pp 406–427

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


DOI: 10.1007/s00453-014-9887-3

Cite this article as:
Boissonnat, JD. & Maria, C. Algorithmica (2014) 70: 406. doi:10.1007/s00453-014-9887-3


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 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.


Simplicial complexes Data structure Computational topology  Flag complexes Witness complexes 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.INRIA Sophia Antipolis-MéditerranéeSophia Antipolis CedexFrance

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