{"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"}],"publisher":"Elsevier","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"10","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"id":"41B58C0C-F248-11E8-B48F-1D18A9856A87","last_name":"Iglesias Ham","first_name":"Mabel","full_name":"Iglesias Ham, Mabel"}],"citation":{"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>.","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.","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.","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>.","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>","short":"H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174."},"title":"Multiple covers with balls II: Weighted averages","project":[{"_id":"255D761E-B435-11E9-9278-68D0E5697425","name":"Topological Complex Systems","call_identifier":"FP7","grant_number":"318493"}],"oa_version":"None","date_published":"2016-10-01T00:00:00Z","page":"169 - 174","date_created":"2018-12-11T11:51:12Z","acknowledgement":"This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme.","scopus_import":1,"department":[{"_id":"HeEd"}],"type":"journal_article","publication":"Electronic Notes in Discrete Mathematics","doi":"10.1016/j.endm.2016.09.030","ec_funded":1,"status":"public","day":"01","date_updated":"2021-01-12T06:49:41Z","_id":"1295","language":[{"iso":"eng"}],"year":"2016","publication_status":"published","quality_controlled":"1","volume":54,"publist_id":"5976","intvolume":"        54"}