{"scopus_import":"1","file":[{"file_id":"5953","creator":"dernst","checksum":"1c8d58cd489a66cd3e2064c1141c8c5e","date_updated":"2020-07-14T12:46:38Z","content_type":"application/pdf","file_size":708357,"relation":"main_file","date_created":"2019-02-12T06:47:52Z","access_level":"open_access","file_name":"2018_Edelsbrunner.pdf"}],"_id":"530","intvolume":" 68","publisher":"Elsevier","ec_funded":1,"title":"Multiple covers with balls I: Inclusion–exclusion","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","full_name":"Iglesias Ham, Mabel","first_name":"Mabel"}],"date_created":"2018-12-11T11:46:59Z","publication":"Computational Geometry: Theory and Applications","status":"public","page":"119 - 133","publist_id":"7289","external_id":{"isi":["000415778300010"]},"corr_author":"1","project":[{"call_identifier":"FP7","name":"Topological Complex Systems","grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"file_date_updated":"2020-07-14T12:46:38Z","language":[{"iso":"eng"}],"doi":"10.1016/j.comgeo.2017.06.014","ddc":["000"],"date_published":"2018-03-01T00:00:00Z","department":[{"_id":"HeEd"}],"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"}],"has_accepted_license":"1","article_processing_charge":"No","year":"2018","volume":68,"type":"journal_article","citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications, vol. 68, Elsevier, 2018, pp. 119–33, doi:10.1016/j.comgeo.2017.06.014.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 2018;68:119-133. doi:10.1016/j.comgeo.2017.06.014","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls I: Inclusion–Exclusion.” Computational Geometry: Theory and Applications. Elsevier, 2018. https://doi.org/10.1016/j.comgeo.2017.06.014.","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” Computational Geometry: Theory and Applications, vol. 68. Elsevier, pp. 119–133, 2018.","ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.","apa":"Edelsbrunner, H., & Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. Elsevier. https://doi.org/10.1016/j.comgeo.2017.06.014"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"03","publication_status":"published","oa":1,"isi":1,"quality_controlled":"1","date_updated":"2025-04-15T08:37:54Z","day":"01","oa_version":"Preprint"}