Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Introduction to Algorithms
GRIN'01 No description on Graphics interface 2001
Removing excess topology from isosurfaces
ACM Transactions on Graphics (TOG)
Discrete & Computational Geometry
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Vines and vineyards by updating persistence in linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Extreme Elevation on a 2-Manifold
Discrete & Computational Geometry
Stability of Persistence Diagrams
Discrete & Computational Geometry
The theory of multidimensional persistence
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
SMI '07 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2007
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
Topology for Computing
Optimal homologous cycles, total unimodularity, and linear programming
Proceedings of the forty-second ACM symposium on Theory of computing
Hardness results for homology localization
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
An iterative algorithm for homology computation on simplicial shapes
Computer-Aided Design
Optimal Homologous Cycles, Total Unimodularity, and Linear Programming
SIAM Journal on Computing
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Minimum cuts and shortest non-separating cycles via homology covers
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
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We develop a method for measuring homology classes. This involves two problems. First, we define the size of a homology class, using ideas from relative homology. Second, we define an optimal basis of a homology group to be the basis whose elements' size have the minimal sum. We provide a greedy algorithm to compute the optimal basis and measure classes in it. The algorithm runs in O(@bn^3log^2n) time, where n is the size of the simplicial complex and @b is the Betti number of the homology group. Finally, we prove the stability of our result. The algorithm can be adapted to measure any given class.