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