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

arXiv 2001.02581 ↗First posted 8 Jan 2020cs.CGcited by 14

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Abstract (arXiv)

This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored in a trie whose nodes are in bijection with the faces of the complex. This data structure allows to efficiently implement a large range of basic operations on simplicial complexes. We provide theoretical complexity analysis as well as detailed experimental results. We more specifically study Rips and witness complexes.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jan 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 2; 2023: 0; 2024: 3; 2025: 2; 2026: 1.

14 papers.

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  1. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 219
  2. 2022Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmarkcited by 11
  3. 2021Topological Measurement of Deep Neural Networks Using Persistent Homologycited by 9
  4. 2024What makes math problems hard for reinforcement learning: a case studycited by 9
  5. 2022Euler Characteristic Curves and Profiles: a stable shape invariant for big data problemscited by 8
  6. 2021Classification based on Topological Data Analysiscited by 2
  7. 2021A Topological Data Analysis Based Classifiercited by 2
  8. 2021Dory: Overcoming Barriers to Computing Persistent Homologycited by 1
  9. 2026TopoPrune: Robust Data Pruning via Unified Latent Space Topologycited by 1
  10. 2021Geometric Model Checking of Continuous Spacecited by 0
  11. 2024Persistent Homology via Ellipsoidscited by 0
  12. 2024A DNN Biophysics Model with Topological and Electrostatic Featurescited by 0
2 more
  1. 2025Classification of Histopathology Slides with Persistent Homology Convolutionscited by 0
  2. 2025Frequent subgraph-based persistent homology for graph classificationcited by 0