{"page":"119 - 133","_id":"530","quality_controlled":"1","file_date_updated":"2020-07-14T12:46:38Z","day":"01","has_accepted_license":"1","ec_funded":1,"month":"03","corr_author":"1","publication_status":"published","date_updated":"2025-04-15T08:37:54Z","article_processing_charge":"No","ddc":["000"],"language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"volume":68,"oa_version":"Preprint","type":"journal_article","isi":1,"oa":1,"publication":"Computational Geometry: Theory and Applications","department":[{"_id":"HeEd"}],"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.","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>.","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>.","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>","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","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>"},"scopus_import":"1","date_published":"2018-03-01T00:00:00Z","project":[{"name":"Topological Complex Systems","call_identifier":"FP7","_id":"255D761E-B435-11E9-9278-68D0E5697425","grant_number":"318493"}],"file":[{"date_updated":"2020-07-14T12:46:38Z","checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","file_size":708357,"creator":"dernst","relation":"main_file","file_id":"5953","access_level":"open_access","date_created":"2019-02-12T06:47:52Z","content_type":"application/pdf","file_name":"2018_Edelsbrunner.pdf"}],"intvolume":"        68","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publist_id":"7289","publisher":"Elsevier","author":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","last_name":"Iglesias Ham","first_name":"Mabel","full_name":"Iglesias Ham, Mabel"}],"title":"Multiple covers with balls I: Inclusion–exclusion","status":"public","doi":"10.1016/j.comgeo.2017.06.014","year":"2018","external_id":{"isi":["000415778300010"]},"date_created":"2018-12-11T11:46:59Z"}