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Building Efficient and Compact Data Structures for Simplicial Complexes

Authors Jean-Daniel Boissonnat, Karthik C. S., Sébastien Tavenas

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Jean-Daniel Boissonnat
Karthik C. S.
Sébastien Tavenas

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Jean-Daniel Boissonnat, Karthik C. S., and Sébastien Tavenas. Building Efficient and Compact Data Structures for Simplicial Complexes. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 642-657, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)


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 Maximal Simplex Tree (MxST) and Simplex Array List (SAL). We analyze the compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List under various settings.
  • Simplicial complex
  • Compact data structures
  • Automaton
  • NP-hard


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