Algorithmica (2017) 79:530–567
Building Efﬁcient and Compact Data Structures
for Simplicial Complexes
· Karthik C. S.
Received: 17 April 2015 / Accepted: 24 August 2016 / Published online: 8 September 2016
© Springer Science+Business Media New York 2016
Abstract The Simplex Tree (ST) is a recently introduced data structure that can
represent abstract simplicial complexes of any dimension and allows efﬁcient imple-
mentation of a large range of basic operations on simplicial complexes. In this paper,
we show how to optimally compress the ST while retaining its functionalities. In addi-
tion, we propose two new data structures called the Maximal Simplex Tree and the
Simplex Array List. We analyze the compressed ST, the Maximal Simplex Tree, and
the Simplex Array List under various settings.
Keywords Simplicial complex · Compact data structures · Automaton · NP-hard
An extended abstract appeared in the proceedings of the 31st International Symposium on Computational
J.-D. Boissonnat: This work was partially supported by the Advanced Grant of the European Research
Council GUDHI (Geometric Understanding in Higher Dimensions).
Karthik C. S.: This work was partially supported by Irit Dinur’s ERC-StG Grant Number 239985. Some
parts of this work were done at ENS Lyon and at University of Nice - Sophia Antipolis, and were
supported by LIP fellowship and Labex UCN@Sophia scholarship respectively.
S. Tavenas: A part of this work was done at LIP, ENS Lyon (UMR 5668 ENS Lyon - CNRS - UCBL -
INRIA, Université de Lyon).
Karthik C. S.
Geometrica, INRIA Sophia Antipolis-Méditerranée, 2004 route des Lucioles, BP 93,
06902 Sophia Antipolis, France
Department of Computer Science and Applied Mathematics, Weizmann Institute of Science,
Microsoft Research India, Bangalore, India