On the complexity of computing the homology type of a triangulation
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Near optimal algorithms for computing Smith normal forms of integer matrices
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Computing Betti numbers via combinatorial Laplacians
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Chaos in the Lorenz equators: a computer assisted proof. part II: details
Mathematics of Computation
Discrete & Computational Geometry
Pattern recognition based on homology theory
Machine Graphics & Vision International Journal
Foundations of Computational Mathematics
Coordinate-free Coverage in Sensor Networks with Controlled Boundaries via Homology
International Journal of Robotics Research
On the detection of simple points in higher dimensions using cubical homology
IEEE Transactions on Image Processing
Digital atlases and difference forms
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Homological Computation Using Spanning Trees
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Detecting pathologies with homology algorithms in magnetic resonance images of brain
Machine Graphics & Vision International Journal
The tidy set: a minimal simplicial set for computing homology of clique complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Decomposing cavities in digital volumes into products of cycles
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Computing homology: a global reduction approach
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Coreduction homology algorithm for inclusions and persistent homology
Computers & Mathematics with Applications
Zigzag persistent homology in matrix multiplication time
Proceedings of the twenty-seventh annual symposium on Computational geometry
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
A fast algorithm to compute cohomology group generators of orientable 2-manifolds
Pattern Recognition Letters
Perfect discrete morse functions on triangulated 3-manifolds
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
Homology computations via acyclic subspace
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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We present a new reduction algorithm for the efficient computation of the homology of a cubical set. The algorithm is based on constructing a possibly large acyclic subspace, and then computing the relative homology instead of the plain homology. We show that the construction of acyclic subspace may be performed in linear time. This significantly reduces the amount of data that needs to be processed in the algebraic way, and in practice it proves itself to be significantly more efficient than other available cubical homology algorithms.