--- res: bibo_abstract: - Persistent homology is the mathematical core of recent work on shape, including reconstruction, recognition, and matching. Its per- tinent information is encapsulated by a pairing of the critical values of a function, visualized by points forming a diagram in the plane. The original algorithm in [10] computes the pairs from an ordering of the simplices in a triangulation and takes worst-case time cubic in the number of simplices. The main result of this paper is an algorithm that maintains the pairing in worst-case linear time per transposition in the ordering. A side-effect of the algorithm’s anal- ysis is an elementary proof of the stability of persistence diagrams [7] in the special case of piecewise-linear functions. We use the algorithm to compute 1-parameter families of diagrams which we apply to the study of protein folding trajectories.@eng bibo_authorlist: - foaf_Person: foaf_givenName: David foaf_name: Cohen-Steiner, David foaf_surname: Cohen Steiner - foaf_Person: foaf_givenName: Herbert foaf_name: Herbert Edelsbrunner foaf_surname: Edelsbrunner foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-9823-6833 - foaf_Person: foaf_givenName: Dmitriy foaf_name: Morozov, Dmitriy foaf_surname: Morozov bibo_doi: 10.1145/1137856.1137877 dct_date: 2006^xs_gYear dct_publisher: ACM@ dct_title: Vines and vineyards by updating persistence in linear time@ ...