Abstract : The Simplex Tree (ST) is a recently introduced data structure
that can represent abstract simplicial complexes of any dimension and
allows efficient implementation of a large range of basic operations on
simplicial complexes. In this paper, we show how to optimally compress
the Simplex Tree while retaining its functionalities. In addition, we
propose two new data structures called the Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the compressed
Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List under various settings.
