, Volume 70, Issue 3, pp 406–427 | Cite as

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

  • Jean-Daniel Boissonnat
  • Clément Maria


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 



The authors thanks A. Ghosh, S. Hornus, D. Morozov and P. Skraba for discussions that led to the idea of representing simplicial complexes by tries. They especially thank S. Hornus for sharing his notes with us. They also thank S. Martin and V. Coutsias for providing the cyclo-octane data set. This research has been partially supported by the 7th Framework Programme for Research of the European Commission, under FET-Open Grant Number 255827 (CGL Computational Geometry Learning).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.INRIA Sophia Antipolis-MéditerranéeSophia Antipolis CedexFrance

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