Ripser: efficient computation of Vietoris–Rips persistence barcodes
Ulrich Bauer
Abstract
Abstract We present an algorithm for the computation of Vietoris–Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage of the filtration coboundary matrix. Moreover, it makes use of apparent pairs, a simple but powerful method for constructing a discrete gradient field from a total order on the simplices of a simplicial complex, which is also of independent interest. Our implementation shows substantial improvements over previous software both in time and memory usage.
Topics & Concepts
ComputationFiltration (mathematics)Computer scienceSoftwareSimple (philosophy)Field (mathematics)Operator (biology)AlgorithmPersistence (discontinuity)MathematicsTheoretical computer scienceMathematical optimizationOrder (exchange)Software systemCode (set theory)Sensitivity (control systems)Computer data storageData structureTopological and Geometric Data AnalysisData Visualization and AnalyticsComputational Geometry and Mesh Generation