---
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 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.@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@
...