{"publication_status":"published","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]},"status":"public","day":"01","ec_funded":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","has_accepted_license":"1","article_type":"original","file":[{"creator":"dernst","file_id":"5932","file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","date_updated":"2020-07-14T12:47:10Z","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","date_created":"2019-02-06T10:10:46Z","access_level":"open_access","content_type":"application/pdf","relation":"main_file","file_size":599339}],"issue":"4","quality_controlled":"1","date_updated":"2024-12-11T11:32:06Z","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"title":"Poisson–Delaunay Mosaics of Order k","corr_author":"1","abstract":[{"lang":"eng","text":"The order-k Voronoi tessellation of a locally finite set 𝑋⊆ℝ𝑛 decomposes ℝ𝑛 into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold."}],"volume":62,"publisher":"Springer","related_material":{"record":[{"status":"public","id":"6287","relation":"dissertation_contains"}]},"publication":"Discrete and Computational Geometry","citation":{"ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” <i>Discrete and Computational Geometry</i>, vol. 62, no. 4. Springer, pp. 865–878, 2019.","chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” <i>Discrete and Computational Geometry</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00454-018-0049-2\">https://doi.org/10.1007/s00454-018-0049-2</a>.","apa":"Edelsbrunner, H., &#38; Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. <i>Discrete and Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-018-0049-2\">https://doi.org/10.1007/s00454-018-0049-2</a>","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” <i>Discrete and Computational Geometry</i>, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:<a href=\"https://doi.org/10.1007/s00454-018-0049-2\">10.1007/s00454-018-0049-2</a>.","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. <i>Discrete and Computational Geometry</i>. 2019;62(4):865–878. doi:<a href=\"https://doi.org/10.1007/s00454-018-0049-2\">10.1007/s00454-018-0049-2</a>"},"arxiv":1,"language":[{"iso":"eng"}],"page":"865–878","date_created":"2018-12-16T22:59:20Z","doi":"10.1007/s00454-018-0049-2","oa":1,"department":[{"_id":"HeEd"}],"isi":1,"scopus_import":"1","year":"2019","month":"12","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"article_processing_charge":"Yes (via OA deal)","file_date_updated":"2020-07-14T12:47:10Z","date_published":"2019-12-01T00:00:00Z","oa_version":"Published Version","ddc":["516"],"author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","full_name":"Nikitenko, Anton","last_name":"Nikitenko","orcid":"0000-0002-0659-3201","first_name":"Anton"}],"type":"journal_article","_id":"5678","intvolume":"        62"}