{"title":"Poisson–Delaunay Mosaics of Order k","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"12","publication_status":"published","department":[{"_id":"HeEd"}],"doi":"10.1007/s00454-018-0049-2","page":"865–878","article_processing_charge":"Yes (via OA deal)","date_created":"2018-12-16T22:59:20Z","issue":"4","oa":1,"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"full_name":"Nikitenko, Anton","last_name":"Nikitenko","first_name":"Anton","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0659-3201"}],"file_date_updated":"2020-07-14T12:47:10Z","publication_identifier":{"eissn":["14320444"],"issn":["01795376"]},"_id":"5678","external_id":{"isi":["000494042900008"],"arxiv":["1709.09380"]},"quality_controlled":"1","intvolume":"        62","publisher":"Springer","corr_author":"1","article_type":"original","date_updated":"2024-10-09T20:58:36Z","publication":"Discrete and Computational Geometry","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6287"}]},"day":"01","status":"public","ec_funded":1,"has_accepted_license":"1","scopus_import":"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."}],"citation":{"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>","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.","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.","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>","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."},"language":[{"iso":"eng"}],"type":"journal_article","ddc":["516"],"volume":62,"year":"2019","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"isi":1,"oa_version":"Published Version","date_published":"2019-12-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"file":[{"access_level":"open_access","creator":"dernst","date_updated":"2020-07-14T12:47:10Z","file_id":"5932","date_created":"2019-02-06T10:10:46Z","relation":"main_file","file_size":599339,"content_type":"application/pdf","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf"}]}