Building Efficient and Compact Data Structures for Simplicial Complexes

TL;DR

This paper introduces optimized compression techniques for the Simplex Tree and proposes two new data structures, the Maximal Simplex Tree and Simplex Array List, enhancing efficiency in representing simplicial complexes.

Contribution

It presents the first optimal compression method for the Simplex Tree and introduces two novel data structures for better representation of simplicial complexes.

Findings

Compressed Simplex Tree retains functionalities efficiently.

Maximal Simplex Tree and SAL outperform existing structures in various settings.

Analysis shows improved space and operation efficiency.

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.