Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
An incremental algorithm for Betti numbers of simplicial complexes
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A computationally intractable problem on simplicial complexes
Computational Geometry: Theory and Applications
Computing Betti numbers via combinatorial Laplacians
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On computing the determinant and Smith form of an integer matrix
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Optimal discrete Morse functions for 2-manifolds
Computational Geometry: Theory and Applications
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Discrete & Computational Geometry
Group-theoretic Algorithms for Matrix Multiplication
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Computing Optimal Morse Matchings
SIAM Journal on Discrete Mathematics
Algebraic Structures and Algorithms for Matching and Matroid Problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Stability of Persistence Diagrams
Discrete & Computational Geometry
Homology algorithm based on acyclic subspace
Computers & Mathematics with Applications
Persistent homology for kernels, images, and cokernels
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Extending Persistence Using Poincaré and Lefschetz Duality
Foundations of Computational Mathematics
Zigzag persistent homology and real-valued functions
Proceedings of the twenty-fifth annual symposium on Computational geometry
Homological illusions of persistence and stability
Homological illusions of persistence and stability
The tidy set: a minimal simplicial set for computing homology of clique complexes
Proceedings of the twenty-sixth annual symposium on Computational geometry
Foundations of Computational Mathematics
An output-sensitive algorithm for persistent homology
Proceedings of the twenty-seventh annual symposium on Computational geometry
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
Geometry in the space of persistence modules
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We present a new algorithm for computing zigzag persistent homology, an algebraic structure which encodes changes to homology groups of a simplicial complex over a sequence of simplex additions and deletions. Provided that there is an algorithm that multiplies two n×n matrices in M(n) time, our algorithm runs in O(M(n) + n2 log2 n) time for a sequence of n additions and deletions. In particular, the running time is O(n2.376), by result of Coppersmith and Winograd. The fastest previously known algorithm for this problem takes O(n3) time in the worst case.