{"citation":{"ista":"Edelsbrunner H, Ölsböck K. 2019. Holes and dependences in an ordered complex. Computer Aided Geometric Design. 73, 1–15.","apa":"Edelsbrunner, H., &#38; Ölsböck, K. (2019). Holes and dependences in an ordered complex. <i>Computer Aided Geometric Design</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">https://doi.org/10.1016/j.cagd.2019.06.003</a>","chicago":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” <i>Computer Aided Geometric Design</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">https://doi.org/10.1016/j.cagd.2019.06.003</a>.","ama":"Edelsbrunner H, Ölsböck K. Holes and dependences in an ordered complex. <i>Computer Aided Geometric Design</i>. 2019;73:1-15. doi:<a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">10.1016/j.cagd.2019.06.003</a>","ieee":"H. Edelsbrunner and K. Ölsböck, “Holes and dependences in an ordered complex,” <i>Computer Aided Geometric Design</i>, vol. 73. Elsevier, pp. 1–15, 2019.","short":"H. Edelsbrunner, K. Ölsböck, Computer Aided Geometric Design 73 (2019) 1–15.","mla":"Edelsbrunner, Herbert, and Katharina Ölsböck. “Holes and Dependences in an Ordered Complex.” <i>Computer Aided Geometric Design</i>, vol. 73, Elsevier, 2019, pp. 1–15, doi:<a href=\"https://doi.org/10.1016/j.cagd.2019.06.003\">10.1016/j.cagd.2019.06.003</a>."},"date_published":"2019-08-01T00:00:00Z","intvolume":"        73","tmp":{"short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"project":[{"grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"}],"title":"Holes and dependences in an ordered complex","quality_controlled":"1","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"7460"}]},"year":"2019","ec_funded":1,"month":"08","date_updated":"2023-09-07T13:15:29Z","oa_version":"Published Version","author":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Ölsböck","orcid":"0000-0002-4672-8297","first_name":"Katharina","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","full_name":"Ölsböck, Katharina"}],"status":"public","external_id":{"isi":["000485207800001"]},"ddc":["000"],"type":"journal_article","has_accepted_license":"1","page":"1-15","doi":"10.1016/j.cagd.2019.06.003","file":[{"file_name":"Elsevier_2019_Edelsbrunner.pdf","creator":"kschuh","file_id":"6624","content_type":"application/pdf","date_updated":"2020-07-14T12:47:34Z","date_created":"2019-07-08T15:24:26Z","access_level":"open_access","checksum":"7c99be505dc7533257d42eb1830cef04","file_size":2665013,"relation":"main_file"}],"department":[{"_id":"HeEd"}],"day":"01","publisher":"Elsevier","article_processing_charge":"No","isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2020-07-14T12:47:34Z","abstract":[{"text":"We use the canonical bases produced by the tri-partition algorithm in (Edelsbrunner and Ölsböck, 2018) to open and close holes in a polyhedral complex, K. In a concrete application, we consider the Delaunay mosaic of a finite set, we let K be an Alpha complex, and we use the persistence diagram of the distance function to guide the hole opening and closing operations. The dependences between the holes define a partial order on the cells in K that characterizes what can and what cannot be constructed using the operations. The relations in this partial order reveal structural information about the underlying filtration of complexes beyond what is expressed by the persistence diagram.","lang":"eng"}],"volume":73,"date_created":"2019-07-07T21:59:20Z","language":[{"iso":"eng"}],"publication":"Computer Aided Geometric Design","publication_status":"published","_id":"6608","oa":1,"scopus_import":"1"}