The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes

DOI10.1007/s00453-014-9887-3zbMath1365.68171arXiv2001.02581OpenAlexW4391060407MaRDI QIDQ134868

Clément Maria, Jean-Daniel Boissonnat, Clément Maria, Jean-Daniel Boissonnat

Publication date: 14 May 2014

Published in: Algorithmica, Algorithms – ESA 2012 (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.02581

zbMATH Keywords

simplicial complexessimplicial complexcomputational topologyflag complexdata structureRips complexflag complexeswitness complexeswitness complexrelaxed witness complex

Mathematics Subject Classification ID

Data structures (68P05) Simplicial sets and complexes in algebraic topology (55U10)

Related Items (20)

interplex ⋮ Algorithmic canonical stratifications of simplicial complexes ⋮ Tracing Isomanifolds in \(\mathbb{R}\) ^d in Time Polynomial in d using Coxeter–Freudenthal–Kuhn Triangulations ⋮ A Probabilistic Approach to Reducing Algebraic Complexity of Delaunay Triangulations ⋮ Geometric Model Checking of Continuous Space ⋮ Building efficient and compact data structures for simplicial complexes ⋮ Barcodes of towers and a streaming algorithm for persistent homology ⋮ The compressed annotation matrix: an efficient data structure for computing persistent cohomology ⋮ Only distances are required to reconstruct submanifolds ⋮ Compression with wildcards: Abstract simplicial complexes ⋮ On the complexity of the representation of simplicial complexes by trees ⋮ Persistent homology for low-complexity models ⋮ The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes ⋮ simplextree ⋮ The Implementation of the Colored Abstract Simplicial Complex and Its Application to Mesh Generation ⋮ \textsc{Phat} -- persistent homology algorithms toolbox ⋮ Topological measurement of deep neural networks using persistent homology ⋮ SimBa ⋮ Approximating persistent homology in Euclidean space through collapses ⋮ Graph induced complex on point data

Uses Software

• Dionysus
• jPlex
• ANN
• Stanford 3D Scanning Repository

Cites Work

• The Simplex Tree: An Efficient Data Structure for General Simplicial Complexes
• The compressed annotation matrix: an efficient data structure for computing persistent cohomology
• On the local behavior of spaces of natural images
• The nonlinear statistics of high-contrast patches in natural images
• Representing geometric structures in \(d\) dimensions: Topology and order
• Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
• Towards persistence-based reconstruction in euclidean spaces
• N-DIMENSIONAL GENERALIZED COMBINATORIAL MAPS AND CELLULAR QUASI-MANIFOLDS
• The tidy set
• Manifold reconstruction in arbitrary dimensions using witness complexes
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