[{"day":"01","file_date_updated":"2019-02-12T06:47:52Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":68,"date_published":"2018-03-01T00:00:00Z","ddc":["000"],"oa_version":"Preprint","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"}],"department":[{"_id":"HeEd"}],"type":"journal_article","page":"119 - 133","language":[{"iso":"eng"}],"month":"03","_id":"530","title":"Multiple covers with balls I: Inclusion–exclusion","status":"public","citation":{"ista":"Edelsbrunner H, Iglesias Ham M. 2018. Multiple covers with balls I: Inclusion–exclusion. Computational Geometry: Theory and Applications. 68, 119–133.","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls I: Inclusion–exclusion,” <i>Computational Geometry: Theory and Applications</i>, vol. 68, 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> 68 (2018): 119–33. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">https://doi.org/10.1016/j.comgeo.2017.06.014</a>.","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>","apa":"Edelsbrunner, H., &#38; Iglesias Ham, M. (2018). Multiple covers with balls I: Inclusion–exclusion. <i>Computational Geometry: Theory and Applications</i>, <i>68</i>, 119–133. <a href=\"https://doi.org/10.1016/j.comgeo.2017.06.014\">https://doi.org/10.1016/j.comgeo.2017.06.014</a>","short":"H. Edelsbrunner, M. Iglesias Ham, Computational Geometry: Theory and Applications 68 (2018) 119–133.","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>."},"date_updated":"2019-02-13T16:11:27Z","publist_id":"7289","accept":"1","publication_status":"published","article_processing_charge":"No","file":[{"content_type":"application/pdf","file_name":"2018_Edelsbrunner.pdf","file_id":"5953","relation":"main_file","date_created":"2019-02-12T06:47:52Z","file_size":708357,"open_access":1,"creator":"dernst","access_level":"open_access","date_updated":"2019-02-12T06:47:52Z","success":1}],"author":[{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel","full_name":"Iglesias Ham, Mabel"}],"project":[{"_id":"FCFDDC1A-FDE9-11E8-8832-D63AE6697425","name":"Topological Complex Systems","grant_number":"318493"}],"publication":"Computational Geometry: Theory and Applications","year":"2018","intvolume":"        68","quality_controlled":"1","date_created":"2018-12-11T11:46:59Z","doi":"10.1016/j.comgeo.2017.06.014","publisher":"Elsevier"}]