Clustering Algorithms
Discrete & Computational Geometry
Vines and vineyards by updating persistence in linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Stability of Persistence Diagrams
Discrete & Computational Geometry
Stability of Critical Points with Interval Persistence
Discrete & Computational Geometry
Persistent homology for kernels, images, and cokernels
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Analysis of scalar fields over point cloud data
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Extending Persistence Using Poincaré and Lefschetz Duality
Foundations of Computational Mathematics
Proximity of persistence modules and their diagrams
Proceedings of the twenty-fifth annual symposium on Computational geometry
Tracking a generator by persistence
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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
Incremental-decremental algorithm for computing AT-models and persistent homology
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Linear-size approximations to the vietoris-rips filtration
Proceedings of the twenty-eighth annual symposium on Computational geometry
Alexander duality for functions: the persistent behavior of land and water and shore
Proceedings of the twenty-eighth annual symposium on Computational geometry
A point calculus for interlevel set homology
Pattern Recognition Letters
An output-sensitive algorithm for persistent homology
Computational Geometry: Theory and Applications
Topological evaluation of volume reconstructions by voxel carving
Computer Vision and Image Understanding
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We study the problem of computing zigzag persistence of a sequence of homology groups and study a particular sequence derived from the levelsets of a real-valued function on a topological space. The result is a local, symmetric interval descriptor of the function. Our structural results establish a connection between the zigzag pairs in this sequence and extended persistence, and in the process resolve an open question associated with the latter. Our algorithmic results not only provide a way to compute zigzag persistence for any sequence of homology groups, but combined with our structural results give a novel algorithm for computing extended persistence. This algorithm is easily parallelizable and uses (asymptotically) less memory.