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. © 2012 Springer-Verlag.
CITATION STYLE
Boissonnat, J. D., & Maria, C. (2012). The simplex tree: An efficient data structure for general simplicial complexes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7501 LNCS, pp. 731–742). https://doi.org/10.1007/978-3-642-33090-2_63
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