# Building Efficient and Compact Data Structures for Simplicial Complexes

arXiv: https://arxiv.org/abs/1503.07444 · HTML: https://mlsanity.com/paper/1503.07444/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2015.

## Built on by (most cited first, 2 of 2)

- [Classification based on Topological Data Analysis](https://mlsanity.com/paper/2102.03709/) (2021)
- [A Topological Data Analysis Based Classifier](https://mlsanity.com/paper/2111.05214/) (2021)

## Abstract (arXiv)

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.