{"date_updated":"2023-10-04T12:03:40Z","file":[{"creator":"cchlebak","success":1,"content_type":"application/pdf","checksum":"71ce7e59f7ee4620acc704fecca620c2","file_size":1359323,"file_name":"2023_DisCompGeo_Corbet.pdf","date_created":"2023-03-07T14:40:14Z","relation":"main_file","date_updated":"2023-03-07T14:40:14Z","access_level":"open_access","file_id":"12715"}],"date_created":"2023-03-05T23:01:06Z","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"page":"376-405","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":70,"oa":1,"tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"publication":"Discrete and Computational Geometry","month":"09","quality_controlled":"1","title":"Computing the multicover bifiltration","scopus_import":"1","oa_version":"Published Version","intvolume":"        70","day":"01","ddc":["000"],"status":"public","publisher":"Springer Nature","type":"journal_article","citation":{"ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. <i>Discrete and Computational Geometry</i>. 2023;70:376-405. doi:<a href=\"https://doi.org/10.1007/s00454-022-00476-8\">10.1007/s00454-022-00476-8</a>","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” <i>Discrete and Computational Geometry</i>, vol. 70, Springer Nature, 2023, pp. 376–405, doi:<a href=\"https://doi.org/10.1007/s00454-022-00476-8\">10.1007/s00454-022-00476-8</a>.","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2023. Computing the multicover bifiltration. Discrete and Computational Geometry. 70, 376–405.","chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00454-022-00476-8\">https://doi.org/10.1007/s00454-022-00476-8</a>.","ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” <i>Discrete and Computational Geometry</i>, vol. 70. Springer Nature, pp. 376–405, 2023.","apa":"Corbet, R., Kerber, M., Lesnick, M., &#38; Osang, G. F. (2023). Computing the multicover bifiltration. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-022-00476-8\">https://doi.org/10.1007/s00454-022-00476-8</a>","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, Discrete and Computational Geometry 70 (2023) 376–405."},"year":"2023","doi":"10.1007/s00454-022-00476-8","external_id":{"arxiv":["2103.07823"],"isi":["000936496800001"]},"date_published":"2023-09-01T00:00:00Z","article_type":"original","abstract":[{"text":"Given a finite set A ⊂ ℝ^d, let Cov_{r,k} denote the set of all points within distance r to at least k points of A. Allowing r and k to vary, we obtain a 2-parameter family of spaces that grow larger when r increases or k decreases, called the multicover bifiltration. Motivated by the problem of computing the homology of this bifiltration, we introduce two closely related combinatorial bifiltrations, one polyhedral and the other simplicial, which are both topologically equivalent to the multicover bifiltration and far smaller than a Čech-based model considered in prior work of Sheehy. Our polyhedral construction is a bifiltration of the rhomboid tiling of Edelsbrunner and Osang, and can be efficiently computed using a variant of an algorithm given by these authors as well. Using an implementation for dimension 2 and 3, we provide experimental results. Our simplicial construction is useful for understanding the polyhedral construction and proving its correctness.","lang":"eng"}],"isi":1,"has_accepted_license":"1","acknowledgement":"We thank the anonymous reviewers for many helpful comments and suggestions, which led to substantial improvements of the paper. The first two authors were supported by the Austrian Science Fund (FWF) grant number P 29984-N35 and W1230. The first author was partly supported by an Austrian Marshall Plan Scholarship, and by the Brummer & Partners MathDataLab. A conference version of this paper was presented at the 37th International Symposium on Computational Geometry (SoCG 2021). Open access funding provided by the Royal Institute of Technology.","related_material":{"record":[{"status":"public","relation":"earlier_version","id":"9605"}]},"author":[{"last_name":"Corbet","first_name":"René","full_name":"Corbet, René"},{"orcid":"0000-0002-8030-9299","last_name":"Kerber","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","full_name":"Kerber, Michael"},{"full_name":"Lesnick, Michael","first_name":"Michael","last_name":"Lesnick"},{"first_name":"Georg F","full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87","last_name":"Osang","orcid":"0000-0002-8882-5116"}],"file_date_updated":"2023-03-07T14:40:14Z","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"}],"publication_status":"published","_id":"12709","article_processing_charge":"Yes (via OA deal)"}