{"isi":1,"volume":68,"date_updated":"2023-09-13T08:59:00Z","type":"journal_article","has_accepted_license":"1","publication_status":"published","publication":"Computational Geometry: Theory and Applications","abstract":[{"lang":"eng","text":"Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of Rn covered by at least k balls in a finite set. We implement two of the formulas in dimension n=3 and report on results obtained with our software."}],"doi":"10.1016/j.comgeo.2017.06.014","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","last_name":"Iglesias Ham","full_name":"Iglesias Ham, Mabel","first_name":"Mabel"}],"_id":"530","citation":{"ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” <i>Computational Geometry: Theory and Applications</i>, vol. 68. Elsevier, pp. 119–133, 2018.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. <i>Computational Geometry: Theory and Applications</i>. 2018;68:119-133. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">10.1016/j.comgeo.2017.06.014</a>","mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” <i>Computational Geometry: Theory and Applications</i>, vol. 68, Elsevier, 2018, pp. 119–33, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">10.1016/j.comgeo.2017.06.014</a>.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","apa":"Edelsbrunner, H., &#38; Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">https://doi.org/10.1016/j.comgeo.2017.06.014</a>","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2018. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">https://doi.org/10.1016/j.comgeo.2017.06.014</a>.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133."},"date_created":"2018-12-11T11:46:59Z","month":"03","article_processing_charge":"No","department":[{"_id":"HeEd"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["000"],"file_date_updated":"2020-07-14T12:46:38Z","oa":1,"page":"119 - 133","status":"public","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"external_id":{"isi":["000415778300010"]},"intvolume":"        68","file":[{"checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","date_created":"2019-02-12T06:47:52Z","file_name":"2018_Edelsbrunner.pdf","relation":"main_file","access_level":"open_access","date_updated":"2020-07-14T12:46:38Z","file_id":"5953","creator":"dernst","content_type":"application/pdf","file_size":708357}],"language":[{"iso":"eng"}],"publist_id":"7289","oa_version":"Preprint","title":"Multiple covers with balls I: Inclusion–exclusion","quality_controlled":"1","scopus_import":"1","date_published":"2018-03-01T00:00:00Z","ec_funded":1,"year":"2018","publisher":"Elsevier","day":"01"}