{"year":"2019","isi":1,"has_accepted_license":"1","publication":"Discrete and Computational Geometry","day":"01","page":"865–878","date_created":"2018-12-16T22:59:20Z","doi":"10.1007/s00454-018-0049-2","date_published":"2019-12-01T00:00:00Z","oa":1,"publisher":"Springer","quality_controlled":"1","citation":{"chicago":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry. Springer, 2019. https://doi.org/10.1007/s00454-018-0049-2.","ista":"Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.","mla":"Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2.","short":"H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.","ieee":"H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4. Springer, pp. 865–878, 2019.","apa":"Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. Springer. https://doi.org/10.1007/s00454-018-0049-2","ama":"Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["1709.09380"],"isi":["000494042900008"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"full_name":"Nikitenko, Anton","orcid":"0000-0002-0659-3201","last_name":"Nikitenko","id":"3E4FF1BA-F248-11E8-B48F-1D18A9856A87","first_name":"Anton"}],"title":"Poisson–Delaunay Mosaics of Order k","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication_status":"published","publication_identifier":{"issn":["01795376"],"eissn":["14320444"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2018_DiscreteCompGeometry_Edelsbrunner.pdf","date_created":"2019-02-06T10:10:46Z","creator":"dernst","file_size":599339,"date_updated":"2020-07-14T12:47:10Z","file_id":"5932","checksum":"f9d00e166efaccb5a76bbcbb4dcea3b4","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"license":"https://creativecommons.org/licenses/by/4.0/","ec_funded":1,"issue":"4","volume":62,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6287"}]},"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 62","month":"12","date_updated":"2023-09-07T12:07:12Z","ddc":["516"],"department":[{"_id":"HeEd"}],"file_date_updated":"2020-07-14T12:47:10Z","_id":"5678","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public"}