Algorithms for subset testing and finding maximal sets
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
The boost graph library: user guide and reference manual
The boost graph library: user guide and reference manual
The flow complex: a data structure for geometric modeling
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Discrete & Computational Geometry
Linear colorings of simplicial complexes and collapsing
Journal of Combinatorial Theory Series A
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
Bioinformatics
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
Computational Geometry: Theory and Applications
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
A barcode shape descriptor for curve point cloud data
Computers and Graphics
Technical Section: Fast construction of the Vietoris-Rips complex
Computers and Graphics
Algorithms and theory of computation handbook
Topological estimation using witness complexes
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Technical Section: Fast construction of the Vietoris-Rips complex
Computers and Graphics
An output-sensitive algorithm for persistent homology
Proceedings of the twenty-seventh annual symposium on Computational geometry
Zigzag persistent homology in matrix multiplication time
Proceedings of the twenty-seventh annual symposium on Computational geometry
Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes
Proceedings of the twenty-seventh annual symposium on Computational geometry
Efficient data structure for representing and simplifying simplicial complexes in high dimensions
Proceedings of the twenty-seventh annual symposium on Computational geometry
Listing all maximal cliques in large sparse real-world graphs
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Algorithmic complexity of finding cross-cycles in flag complexes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
The simplex tree: an efficient data structure for general simplicial complexes
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
Vietoris-Rips complexes also provide topologically correct reconstructions of sampled shapes
Computational Geometry: Theory and Applications
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We introduce the tidy set, a minimal simplicial set that captures the topology of a simplicial complex. The tidy set is particularly effective for computing the homology of clique complexes. This family of complexes include the Vietoris-Rips complex and the weak witness complex, methods that are popular in topological data analysis. The key feature of our approach is that it skips constructing the clique complex. We give algorithms for constructing tidy sets, implement them, and present experiments. Our preliminary results show that tidy sets are orders of magnitude smaller than clique complexes, giving us a homology engine with small memory requirements.