--- _id: '12086' abstract: - lang: eng text: We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets. acknowledgement: Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Georg F full_name: Osang, Georg F id: 464B40D6-F248-11E8-B48F-1D18A9856A87 last_name: Osang citation: ama: Edelsbrunner H, Osang GF. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 2023;85:277-295. doi:10.1007/s00453-022-01027-6 apa: Edelsbrunner, H., & Osang, G. F. (2023). A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. Springer Nature. https://doi.org/10.1007/s00453-022-01027-6 chicago: Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica. Springer Nature, 2023. https://doi.org/10.1007/s00453-022-01027-6. ieee: H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay mosaics and alpha shapes,” Algorithmica, vol. 85. Springer Nature, pp. 277–295, 2023. ista: Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 85, 277–295. mla: Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” Algorithmica, vol. 85, Springer Nature, 2023, pp. 277–95, doi:10.1007/s00453-022-01027-6. short: H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295. date_created: 2022-09-11T22:01:57Z date_published: 2023-01-01T00:00:00Z date_updated: 2023-06-27T12:53:43Z day: '01' ddc: - '510' department: - _id: HeEd doi: 10.1007/s00453-022-01027-6 ec_funded: 1 external_id: isi: - '000846967100001' file: - access_level: open_access checksum: 71685ca5121f4c837f40c3f8eb50c915 content_type: application/pdf creator: dernst date_created: 2023-01-20T10:02:48Z date_updated: 2023-01-20T10:02:48Z file_id: '12322' file_name: 2023_Algorithmica_Edelsbrunner.pdf file_size: 911017 relation: main_file success: 1 file_date_updated: 2023-01-20T10:02:48Z has_accepted_license: '1' intvolume: ' 85' isi: 1 language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 277-295 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 268116B8-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z00342 name: The Wittgenstein Prize - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Algorithmica publication_identifier: eissn: - 1432-0541 issn: - 0178-4617 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A simple algorithm for higher-order Delaunay mosaics and alpha shapes tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2EBD1598-F248-11E8-B48F-1D18A9856A87 volume: 85 year: '2023' ...