{"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6287"}]},"status":"public","quality_controlled":"1","title":"Poisson–Delaunay Mosaics of Order k","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2018-12-16T22:59:20Z","oa":1,"oa_version":"Published Version","scopus_import":"1","publisher":"Springer","issue":"4","date_published":"2019-12-01T00:00:00Z","publication_status":"published","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."}],"department":[{"_id":"HeEd"}],"day":"01","file":[{"date_updated":"2020-07-14T12:47:10Z","file_id":"5932","file_size":599339,"date_created":"2019-02-06T10:10:46Z","relation":"main_file","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","content_type":"application/pdf","file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","access_level":"open_access","creator":"dernst"}],"type":"journal_article","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2023-09-07T12:07:12Z","article_processing_charge":"Yes (via OA deal)","month":"12","isi":1,"file_date_updated":"2020-07-14T12:47:10Z","ddc":["516"],"project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020"},{"grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"volume":62,"intvolume":"        62","year":"2019","ec_funded":1,"citation":{"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>","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>.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","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>","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","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>.","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."},"article_type":"original","language":[{"iso":"eng"}],"_id":"5678","doi":"10.1007/s00454-018-0049-2","page":"865–878","has_accepted_license":"1","publication":"Discrete and Computational Geometry","author":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"},{"orcid":"0000-0002-0659-3201","full_name":"Nikitenko, Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","last_name":"Nikitenko","first_name":"Anton"}],"publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]}}