{"id":"https://openalex.org/W2506035431","doi":"https://doi.org/10.1007/s00454-017-9885-8","title":"On Sets Defining Few Ordinary Circles","display_name":"On Sets Defining Few Ordinary Circles","publication_year":2017,"publication_date":"2017-03-20","ids":{"openalex":"https://openalex.org/W2506035431","doi":"https://doi.org/10.1007/s00454-017-9885-8","mag":"2506035431","pmid":"https://pubmed.ncbi.nlm.nih.gov/29284799"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-017-9885-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9885-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9885-8.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9885-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031290514","display_name":"Aaron Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Aaron Lin","raw_affiliation_strings":["Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE United Kingdom","Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE United Kingdom","institution_ids":["https://openalex.org/I909854389"]},{"raw_affiliation_string":"Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE, United Kingdom","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013629904","display_name":"Mehdi Makhul","orcid":"https://orcid.org/0000-0001-7887-1955"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Mehdi Makhul","raw_affiliation_strings":["Research Institute for Symbolic Computation, Johannes Kepler University, 4040 Linz, Austria","Research Institute for Symbolic Computation, Johannes Kepler University, 4040, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute for Symbolic Computation, Johannes Kepler University, 4040 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]},{"raw_affiliation_string":"Research Institute for Symbolic Computation, Johannes Kepler University, 4040, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004392809","display_name":"Hossein Nassajian Mojarrad","orcid":"https://orcid.org/0000-0003-0741-6060"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Hossein Nassajian Mojarrad","raw_affiliation_strings":["Department of Mathematics, EPFL, 1015 Lausanne, Switzerland","Department of Mathematics, EPFL, 1015, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, EPFL, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Department of Mathematics, EPFL, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072589415","display_name":"Josef Schicho","orcid":"https://orcid.org/0000-0002-5556-4001"},"institutions":[{"id":"https://openalex.org/I121883995","display_name":"Johannes Kepler University of Linz","ror":"https://ror.org/052r2xn60","country_code":"AT","type":"education","lineage":["https://openalex.org/I121883995"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Josef Schicho","raw_affiliation_strings":["Research Institute for Symbolic Computation, Johannes Kepler University, 4040 Linz, Austria","Research Institute for Symbolic Computation, Johannes Kepler University, 4040, Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Institute for Symbolic Computation, Johannes Kepler University, 4040 Linz, Austria","institution_ids":["https://openalex.org/I121883995"]},{"raw_affiliation_string":"Research Institute for Symbolic Computation, Johannes Kepler University, 4040, Linz, Austria","institution_ids":["https://openalex.org/I121883995"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050925265","display_name":"Konrad J. Swanepoel","orcid":"https://orcid.org/0000-0002-1668-887X"},"institutions":[{"id":"https://openalex.org/I909854389","display_name":"London School of Economics and Political Science","ror":"https://ror.org/0090zs177","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I909854389"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Konrad Swanepoel","raw_affiliation_strings":["Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE United Kingdom","Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE United Kingdom","institution_ids":["https://openalex.org/I909854389"]},{"raw_affiliation_string":"Department of Mathematics, London School of Economics and Political Science, London, WC2A 2AE, United Kingdom","institution_ids":["https://openalex.org/I909854389"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069319850","display_name":"Frank de Zeeuw","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Frank de Zeeuw","raw_affiliation_strings":["Department of Mathematics, EPFL, 1015 Lausanne, Switzerland","Department of Mathematics, EPFL, 1015, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, EPFL, 1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"Department of Mathematics, EPFL, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":3.6644,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.92169312,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"59","issue":"1","first_page":"59","last_page":"87"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9977999925613403,"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":0.9977999925613403,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7907723188400269},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6513960361480713},{"id":"https://openalex.org/keywords/algebraic-curve","display_name":"Algebraic curve","score":0.5266040563583374},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4620674252510071},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4543953239917755},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4488445222377777},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.44827884435653687},{"id":"https://openalex.org/keywords/circle-graph","display_name":"Circle graph","score":0.43340060114860535},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3335034251213074},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.273742139339447},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21506565809249878},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21389099955558777},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08841690421104431},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.07587581872940063}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7907723188400269},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6513960361480713},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.5266040563583374},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4620674252510071},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4543953239917755},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4488445222377777},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.44827884435653687},{"id":"https://openalex.org/C171528893","wikidata":"https://www.wikidata.org/wiki/Q5121450","display_name":"Circle graph","level":5,"score":0.43340060114860535},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3335034251213074},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.273742139339447},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21506565809249878},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21389099955558777},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08841690421104431},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.07587581872940063},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s00454-017-9885-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9885-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9885-8.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1607.06597","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.06597","pdf_url":"https://arxiv.org/pdf/1607.06597","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmid:29284799","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29284799","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & computational geometry","raw_type":null},{"id":"pmh:oai:eprints.lse.ac.uk:69645","is_oa":true,"landing_page_url":"https://orcid.org/0000-0002-1668-887X>","pdf_url":"http://eprints.lse.ac.uk/69645/7/Swanepoel_On%20sets%20defining%20few%20ordinary%20circles_published_2017%20LSERO.pdf","source":{"id":"https://openalex.org/S4306401593","display_name":"London School of Economics and Political Science Research Online (London School of Economics and Political Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I909854389","host_organization_name":"London School of Economics and Political Science","host_organization_lineage":["https://openalex.org/I909854389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:europepmc.org:4653857","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5735220","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:infoscience.epfl.ch:234053","is_oa":false,"landing_page_url":"http://infoscience.epfl.ch/record/234053","pdf_url":null,"source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:infoscience.tind.io:234053","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/144001","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"research article"}],"best_oa_location":{"id":"doi:10.1007/s00454-017-9885-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9885-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9885-8.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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1530265356","display_name":"Decompositions and Transversals of Geometric Arrangements","funder_award_id":"162884","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G296353214","display_name":null,"funder_award_id":"200021-162884","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4782960262","display_name":null,"funder_award_id":"200020-165977","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5256785375","display_name":null,"funder_award_id":"200021-","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5599649393","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G628552264","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G8127242481","display_name":"Geometric intersection graphs and hypergraphs","funder_award_id":"165977","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2506035431.pdf","grobid_xml":"https://content.openalex.org/works/W2506035431.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W146075194","https://openalex.org/W617067223","https://openalex.org/W1482692454","https://openalex.org/W1486898453","https://openalex.org/W1539895965","https://openalex.org/W1640777235","https://openalex.org/W1982150165","https://openalex.org/W2000025325","https://openalex.org/W2005740603","https://openalex.org/W2026745357","https://openalex.org/W2029090149","https://openalex.org/W2053849387","https://openalex.org/W2058401132","https://openalex.org/W2061788258","https://openalex.org/W2078079767","https://openalex.org/W2112876384","https://openalex.org/W2412178246","https://openalex.org/W2489723062","https://openalex.org/W2740360930","https://openalex.org/W2797575672","https://openalex.org/W2798442789","https://openalex.org/W2963195447","https://openalex.org/W2963888357","https://openalex.org/W3143314279","https://openalex.org/W4239754742","https://openalex.org/W4240897641","https://openalex.org/W4241628619","https://openalex.org/W4252300791","https://openalex.org/W4252725080","https://openalex.org/W4292027090","https://openalex.org/W4292482156","https://openalex.org/W4299615030"],"related_works":["https://openalex.org/W2399035783","https://openalex.org/W3161230432","https://openalex.org/W1487201914","https://openalex.org/W4367190712","https://openalex.org/W280458463","https://openalex.org/W1170131723","https://openalex.org/W4301429470","https://openalex.org/W4311528773","https://openalex.org/W4296545099","https://openalex.org/W4390784559"],"abstract_inverted_index":{"An":[0],"ordinary":[1,48,58],"circle":[2,17,80],"of":[3,7,23,57,82,105],"a":[4,16,34,37],"set":[5],"P":[6,29,40,89],"n":[8,44,64,93],"points":[9,22,104],"in":[10,33],"the":[11,53,79,83,110,114,127],"plane":[12],"is":[13,30],"defined":[14],"as":[15],"that":[18,27,70,88],"contains":[19],"exactly":[20,102],"three":[21],"P.":[24,106],"We":[25,76,86],"show":[26],"if":[28],"not":[31],"contained":[32],"line":[35],"or":[36],"circle,":[38],"then":[39],"spans":[41,90],"at":[42,91],"least":[43],"2":[45,97],"/4":[46],"-O(n)":[47],"circles.":[49],"Moreover,":[50],"we":[51,108],"determine":[52,109],"exact":[54,111],"minimum":[55],"number":[56],"circles":[59,99],"for":[60,117],"all":[61,67,118],"sufficiently":[62,119],"large":[63,120],"and":[65,113],"describe":[66],"point":[68],"sets":[69],"come":[71],"close":[72],"to":[73],"this":[74],"minimum.":[75],"also":[77],"consider":[78],"variant":[81],"orchard":[84],"problem.":[85],"prove":[87],"most":[92],"3":[94],"/24":[95],"-O(n":[96],")":[98],"passing":[100],"through":[101],"four":[103],"Here":[107],"maximum":[112],"extremal":[115],"configurations":[116],"n.":[121],"These":[122],"results":[123],"are":[124],"based":[125],"on":[126]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2020-11-23T00:00:00"}
