Building Efficient and Compact Data Structures for Simplicial Complexe

Jean-Daniel Boissonnat (1) , Karthik C. Srikanta (2) , Sébastien Tavenas (3)

1 DATASHAPE - Understanding the Shape of Data
2 Weizmann Institute of Science [Rehovot, Israël]
3 MC2 - Modèles de calcul, Complexité, Combinatoire

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.

Mots clés: Simplicial complex; Compact data structures; Automaton; NP-hard

Domaines: Géométrie algorithmique [cs.CG]

Jean-Daniel Boissonnat, Karthik C. Srikanta, Sébastien Tavenas. Building Efficient and Compact Data Structures for Simplicial Complexe. Algorithmica, 2016, ⟨10.1007/s00453-016-0207-y⟩. ⟨hal-01364648⟩