{"acknowledgement":"Partially supported by NSF under grant CCR- 00-86013, by DARPA under grant HR0011-05-1-0007, and by the Lawrence Livermore National Laboratory under grant B543154.","conference":{"name":"SCG: Symposium on Computational Geometry"},"date_published":"2006-06-01T00:00:00Z","status":"public","abstract":[{"lang":"eng","text":"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."}],"publication_status":"published","type":"conference","publist_id":"2826","month":"06","citation":{"mla":"Cohen Steiner, David, et al. <i>Vines and Vineyards by Updating Persistence in Linear Time</i>. ACM, 2006, pp. 119–26, doi:<a href=\"https://doi.org/10.1145/1137856.1137877\">10.1145/1137856.1137877</a>.","ista":"Cohen Steiner D, Edelsbrunner H, Morozov D. 2006. Vines and vineyards by updating persistence in linear time. SCG: Symposium on Computational Geometry, 119–126.","short":"D. Cohen Steiner, H. Edelsbrunner, D. Morozov, in:, ACM, 2006, pp. 119–126.","ieee":"D. Cohen Steiner, H. Edelsbrunner, and D. Morozov, “Vines and vineyards by updating persistence in linear time,” presented at the SCG: Symposium on Computational Geometry, 2006, pp. 119–126.","chicago":"Cohen Steiner, David, Herbert Edelsbrunner, and Dmitriy Morozov. “Vines and Vineyards by Updating Persistence in Linear Time,” 119–26. ACM, 2006. <a href=\"https://doi.org/10.1145/1137856.1137877\">https://doi.org/10.1145/1137856.1137877</a>.","ama":"Cohen Steiner D, Edelsbrunner H, Morozov D. Vines and vineyards by updating persistence in linear time. In: ACM; 2006:119-126. doi:<a href=\"https://doi.org/10.1145/1137856.1137877\">10.1145/1137856.1137877</a>","apa":"Cohen Steiner, D., Edelsbrunner, H., &#38; Morozov, D. (2006). Vines and vineyards by updating persistence in linear time (pp. 119–126). Presented at the SCG: Symposium on Computational Geometry, ACM. <a href=\"https://doi.org/10.1145/1137856.1137877\">https://doi.org/10.1145/1137856.1137877</a>"},"publisher":"ACM","extern":1,"year":"2006","day":"01","_id":"3559","page":"119 - 126","doi":"10.1145/1137856.1137877","quality_controlled":0,"date_created":"2018-12-11T12:03:58Z","date_updated":"2021-01-12T07:44:18Z","author":[{"first_name":"David","last_name":"Cohen Steiner","full_name":"Cohen-Steiner, David"},{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Herbert Edelsbrunner"},{"full_name":"Morozov, Dmitriy","first_name":"Dmitriy","last_name":"Morozov"}],"title":"Vines and vineyards by updating persistence in linear time"}