--- _id: '1295' abstract: - lang: eng 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. acknowledgement: This work is partially supported by the Toposys project FP7-ICT-318493-STREP, and by ESF under the ACAT Research Network Programme. author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Mabel full_name: Iglesias Ham, Mabel id: 41B58C0C-F248-11E8-B48F-1D18A9856A87 last_name: Iglesias Ham citation: ama: 'Edelsbrunner H, Iglesias Ham M. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 2016;54:169-174. doi:10.1016/j.endm.2016.09.030' apa: 'Edelsbrunner, H., & Iglesias Ham, M. (2016). Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. Elsevier. https://doi.org/10.1016/j.endm.2016.09.030' chicago: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.endm.2016.09.030.' ieee: 'H. Edelsbrunner and M. Iglesias Ham, “Multiple covers with balls II: Weighted averages,” Electronic Notes in Discrete Mathematics, vol. 54. Elsevier, pp. 169–174, 2016.' ista: 'Edelsbrunner H, Iglesias Ham M. 2016. Multiple covers with balls II: Weighted averages. Electronic Notes in Discrete Mathematics. 54, 169–174.' mla: 'Edelsbrunner, Herbert, and Mabel Iglesias Ham. “Multiple Covers with Balls II: Weighted Averages.” Electronic Notes in Discrete Mathematics, vol. 54, Elsevier, 2016, pp. 169–74, doi:10.1016/j.endm.2016.09.030.' short: H. Edelsbrunner, M. Iglesias Ham, Electronic Notes in Discrete Mathematics 54 (2016) 169–174. date_created: 2018-12-11T11:51:12Z date_published: 2016-10-01T00:00:00Z date_updated: 2021-01-12T06:49:41Z day: '01' department: - _id: HeEd doi: 10.1016/j.endm.2016.09.030 ec_funded: 1 intvolume: ' 54' language: - iso: eng month: '10' oa_version: None page: 169 - 174 project: - _id: 255D761E-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '318493' name: Topological Complex Systems publication: Electronic Notes in Discrete Mathematics publication_status: published publisher: Elsevier publist_id: '5976' quality_controlled: '1' scopus_import: 1 status: public title: 'Multiple covers with balls II: Weighted averages' type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 54 year: '2016' ...