{"language":[{"iso":"eng"}],"publist_id":"5007","oa_version":"Submitted Version","main_file_link":[{"url":"http://arxiv.org/abs/1303.0477","open_access":"1"}],"title":"Clear and Compress: Computing Persistent Homology in Chunks","scopus_import":1,"series_title":"Mathematics and Visualization","quality_controlled":"1","editor":[{"first_name":"Peer-Timo","full_name":"Bremer, Peer-Timo","last_name":"Bremer"},{"last_name":"Hotz","full_name":"Hotz, Ingrid","first_name":"Ingrid"},{"first_name":"Valerio","full_name":"Pascucci, Valerio","last_name":"Pascucci"},{"last_name":"Peikert","first_name":"Ronald","full_name":"Peikert, Ronald"}],"date_published":"2014-03-19T00:00:00Z","ec_funded":1,"publisher":"Springer","year":"2014","day":"19","date_updated":"2021-01-12T06:54:56Z","type":"book_chapter","publication_status":"published","publication":"Topological Methods in Data Analysis and Visualization III","abstract":[{"lang":"eng","text":"We present a parallel algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then simplifying the unpaired columns, and finally applying standard reduction on the simplified matrix. The approach generalizes a technique by Günther et al., which uses discrete Morse Theory to compute persistence; we derive the same worst-case complexity bound in a more general context. The algorithm employs several practical optimization techniques, which are of independent interest. Our sequential implementation of the algorithm is competitive with state-of-the-art methods, and we further improve the performance through parallel computation."}],"doi":"10.1007/978-3-319-04099-8_7","author":[{"first_name":"Ulrich","full_name":"Bauer, Ulrich","orcid":"0000-0002-9683-0724","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Kerber, Michael","first_name":"Michael","orcid":"0000-0002-8030-9299","last_name":"Kerber"},{"id":"4505473A-F248-11E8-B48F-1D18A9856A87","last_name":"Reininghaus","first_name":"Jan","full_name":"Reininghaus, Jan"}],"_id":"2044","citation":{"ieee":"U. Bauer, M. Kerber, and J. Reininghaus, “Clear and Compress: Computing Persistent Homology in Chunks,” in <i>Topological Methods in Data Analysis and Visualization III</i>, P.-T. Bremer, I. Hotz, V. Pascucci, and R. Peikert, Eds. Springer, 2014, pp. 103–117.","mla":"Bauer, Ulrich, et al. “Clear and Compress: Computing Persistent Homology in Chunks.” <i>Topological Methods in Data Analysis and Visualization III</i>, edited by Peer-Timo Bremer et al., Springer, 2014, pp. 103–17, doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">10.1007/978-3-319-04099-8_7</a>.","ama":"Bauer U, Kerber M, Reininghaus J. Clear and Compress: Computing Persistent Homology in Chunks. In: Bremer P-T, Hotz I, Pascucci V, Peikert R, eds. <i>Topological Methods in Data Analysis and Visualization III</i>. Mathematics and Visualization. Springer; 2014:103-117. doi:<a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">10.1007/978-3-319-04099-8_7</a>","short":"U. Bauer, M. Kerber, J. Reininghaus, in:, P.-T. Bremer, I. Hotz, V. Pascucci, R. Peikert (Eds.), Topological Methods in Data Analysis and Visualization III, Springer, 2014, pp. 103–117.","apa":"Bauer, U., Kerber, M., &#38; Reininghaus, J. (2014). Clear and Compress: Computing Persistent Homology in Chunks. In P.-T. Bremer, I. Hotz, V. Pascucci, &#38; R. Peikert (Eds.), <i>Topological Methods in Data Analysis and Visualization III</i> (pp. 103–117). Springer. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">https://doi.org/10.1007/978-3-319-04099-8_7</a>","chicago":"Bauer, Ulrich, Michael Kerber, and Jan Reininghaus. “Clear and Compress: Computing Persistent Homology in Chunks.” In <i>Topological Methods in Data Analysis and Visualization III</i>, edited by Peer-Timo Bremer, Ingrid Hotz, Valerio Pascucci, and Ronald Peikert, 103–17. Mathematics and Visualization. Springer, 2014. <a href=\"https://doi.org/10.1007/978-3-319-04099-8_7\">https://doi.org/10.1007/978-3-319-04099-8_7</a>.","ista":"Bauer U, Kerber M, Reininghaus J. 2014.Clear and Compress: Computing Persistent Homology in Chunks. In: Topological Methods in Data Analysis and Visualization III. , 103–117."},"date_created":"2018-12-11T11:55:23Z","month":"03","department":[{"_id":"HeEd"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa":1,"page":"103 - 117","status":"public","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7"}]}