{"abstract":[{"text":"Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voronoi diagrams of average balls.","lang":"eng"}],"publication":"Electronic Notes in Discrete Mathematics","author":[{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Iglesias Ham, Mabel","last_name":"Iglesias Ham","id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","first_name":"Mabel"}],"_id":"1295","publisher":"Elsevier","title":"Multiple covers with balls II: Weighted averages","department":[{"_id":"HeEd"}],"intvolume":"        54","publication_status":"published","type":"journal_article","acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.","quality_controlled":"1","language":[{"iso":"eng"}],"project":[{"call_identifier":"FP7","grant_number":"318493","name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425"}],"status":"public","month":"10","year":"2016","day":"01","corr_author":"1","ec_funded":1,"date_published":"2016-10-01T00:00:00Z","page":"169 - 174","citation":{"mla":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” <i>Electronic Notes in Discrete Mathematics</i>, vol. 54, Elsevier, 2016, pp. 169–74, doi:<a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">10.1016/j.endm.2016.09.030</a>.","short":"H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174.","ama":"Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. <i>Electronic Notes in Discrete Mathematics</i>. 2016;54:169-174. doi:<a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">10.1016/j.endm.2016.09.030</a>","ista":"Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174.","apa":"Edelsbrunner, H., &#38; Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. <i>Electronic Notes in Discrete Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">https://doi.org/10.1016/j.endm.2016.09.030</a>","ieee":"H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” <i>Electronic Notes in Discrete Mathematics</i>, vol. 54. Elsevier, pp. 169–174, 2016.","chicago":"Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” <i>Electronic Notes in Discrete Mathematics</i>. Elsevier, 2016. <a href=\"https://doi.org/10.1016/j.endm.2016.09.030\">https://doi.org/10.1016/j.endm.2016.09.030</a>."},"date_updated":"2024-10-09T20:57:05Z","doi":"10.1016/j.endm.2016.09.030","publist_id":"5976","volume":54,"oa_version":"None","date_created":"2018-12-11T11:51:12Z","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","scopus_import":1}