{"id":"https://openalex.org/W2094650250","doi":"https://doi.org/10.1007/bf02574692","title":"On levels in arrangements and voronoi diagrams","display_name":"On levels in arrangements and voronoi diagrams","publication_year":1991,"publication_date":"1991-09-01","ids":{"openalex":"https://openalex.org/W2094650250","doi":"https://doi.org/10.1007/bf02574692","mag":"2094650250"},"language":"en","primary_location":{"id":"doi:10.1007/bf02574692","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02574692","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02574692.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/BF02574692.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028134406","display_name":"Ketan Mulmuley","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ketan Mulmuley","raw_affiliation_strings":["Department of Computer Science, University of Chicago, 60637, Chicago, IL, USA","Department of Computer Science, University of Chicago, Chicago, USA 60637#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Chicago, 60637, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"Department of Computer Science, University of Chicago, Chicago, USA 60637#TAB#","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028134406"],"corresponding_institution_ids":["https://openalex.org/I40347166"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":6.7607,"has_fulltext":true,"cited_by_count":78,"citation_normalized_percentile":{"value":0.97868713,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"6","issue":"3","first_page":"307","last_page":"338"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12698","display_name":"3D Modeling in Geospatial Applications","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/voronoi-diagram","display_name":"Voronoi diagram","score":0.931462287902832},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.9036669731140137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7659469246864319},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6561181545257568},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6266986131668091},{"id":"https://openalex.org/keywords/discrete-geometry","display_name":"Discrete geometry","score":0.5523602366447449},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.545847475528717},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5043050050735474},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"Computational geometry","score":0.4689364433288574},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33228588104248047},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2738984227180481},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11459705233573914}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.931462287902832},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.9036669731140137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7659469246864319},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6561181545257568},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6266986131668091},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.5523602366447449},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.545847475528717},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5043050050735474},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.4689364433288574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33228588104248047},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2738984227180481},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11459705233573914},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02574692","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02574692","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02574692.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/bf02574692","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02574692","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02574692.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.46000000834465027}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2094650250.pdf","grobid_xml":"https://content.openalex.org/works/W2094650250.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W117619795","https://openalex.org/W1963636442","https://openalex.org/W1974821267","https://openalex.org/W1984406695","https://openalex.org/W1989891686","https://openalex.org/W1996570135","https://openalex.org/W2004358658","https://openalex.org/W2011699817","https://openalex.org/W2028416480","https://openalex.org/W2035774625","https://openalex.org/W2036972043","https://openalex.org/W2052393177","https://openalex.org/W2057335678","https://openalex.org/W2058432138","https://openalex.org/W2067631433","https://openalex.org/W2087686013","https://openalex.org/W2095339735","https://openalex.org/W2102902634","https://openalex.org/W2109067131","https://openalex.org/W2120934134","https://openalex.org/W2145494964","https://openalex.org/W2752853835","https://openalex.org/W2752908210","https://openalex.org/W2911302472","https://openalex.org/W3144496617"],"related_works":["https://openalex.org/W2908074373","https://openalex.org/W130987260","https://openalex.org/W2962789953","https://openalex.org/W1492333335","https://openalex.org/W4250008887","https://openalex.org/W2189603398","https://openalex.org/W1978666516","https://openalex.org/W889844791","https://openalex.org/W2042426695","https://openalex.org/W2054736321"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}