@inproceedings{3559,
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 algorithmâ€™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.},
author = {Cohen-Steiner, David and Herbert Edelsbrunner and Morozov, Dmitriy},
pages = {119 -- 126},
publisher = {ACM},
title = {{Vines and vineyards by updating persistence in linear time}},
doi = {10.1145/1137856.1137877},
year = {2006},
}