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.

中文翻译：

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单纯形树：一般单纯形复形的有效数据结构

本文介绍了一种称为单纯形树的数据结构，用于表示任意维度的抽象单纯形复形。单纯复形的所有面都显式地存储在一个树中，其节点与复形的面双射。这种数据结构允许在单纯复形上有效地实现大范围的基本操作。我们提供理论复杂性分析以及详细的实验结果。我们更具体地研究撕裂和见证情结。