{"file_date_updated":"2021-06-28T12:40:47Z","acknowledgement":"The authors want to thank the reviewers for many helpful comments and suggestions.","ddc":["516"],"volume":189,"intvolume":"       189","year":"2021","citation":{"ieee":"R. Corbet, M. Kerber, M. Lesnick, and G. F. Osang, “Computing the multicover bifiltration,” in <i>Leibniz International Proceedings in Informatics</i>, Online, 2021, vol. 189.","mla":"Corbet, René, et al. “Computing the Multicover Bifiltration.” <i>Leibniz International Proceedings in Informatics</i>, vol. 189, 27, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.27\">10.4230/LIPIcs.SoCG.2021.27</a>.","short":"R. Corbet, M. Kerber, M. Lesnick, G.F. Osang, in:, Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021.","apa":"Corbet, R., Kerber, M., Lesnick, M., &#38; Osang, G. F. (2021). Computing the multicover bifiltration. In <i>Leibniz International Proceedings in Informatics</i> (Vol. 189). Online: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.27\">https://doi.org/10.4230/LIPIcs.SoCG.2021.27</a>","ista":"Corbet R, Kerber M, Lesnick M, Osang GF. 2021. Computing the multicover bifiltration. Leibniz International Proceedings in Informatics. SoCG: International Symposium on Computational Geometry, LIPIcs, vol. 189, 27.","chicago":"Corbet, René, Michael Kerber, Michael Lesnick, and Georg F Osang. “Computing the Multicover Bifiltration.” In <i>Leibniz International Proceedings in Informatics</i>, Vol. 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.27\">https://doi.org/10.4230/LIPIcs.SoCG.2021.27</a>.","ama":"Corbet R, Kerber M, Lesnick M, Osang GF. Computing the multicover bifiltration. In: <i>Leibniz International Proceedings in Informatics</i>. Vol 189. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2021. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2021.27\">10.4230/LIPIcs.SoCG.2021.27</a>"},"conference":{"location":"Online","end_date":"2021-06-11","start_date":"2021-06-07","name":"SoCG: International Symposium on Computational Geometry"},"language":[{"iso":"eng"}],"_id":"9605","article_number":"27","doi":"10.4230/LIPIcs.SoCG.2021.27","has_accepted_license":"1","publication":"Leibniz International Proceedings in Informatics","author":[{"full_name":"Corbet, René","first_name":"René","last_name":"Corbet"},{"full_name":"Kerber, Michael","last_name":"Kerber","first_name":"Michael"},{"full_name":"Lesnick, Michael","last_name":"Lesnick","first_name":"Michael"},{"id":"464B40D6-F248-11E8-B48F-1D18A9856A87","full_name":"Osang, Georg F","first_name":"Georg F","last_name":"Osang","orcid":"0000-0002-8882-5116"}],"publication_identifier":{"isbn":["9783959771849"],"issn":["18688969"]},"external_id":{"arxiv":["2103.07823"]},"related_material":{"link":[{"relation":"extended_version","url":"https://arxiv.org/abs/2103.07823"}],"record":[{"status":"public","relation":"later_version","id":"12709"}]},"status":"public","quality_controlled":"1","title":"Computing the multicover bifiltration","alternative_title":["LIPIcs"],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","date_created":"2021-06-27T22:01:49Z","oa":1,"oa_version":"Published Version","scopus_import":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","publication_status":"published","date_published":"2021-06-02T00:00:00Z","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. 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