The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes
arXiv:2001.02581 · doi:10.1007/s00453-014-9887-3
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.