{"id":"https://openalex.org/W2136361847","doi":"https://doi.org/10.1007/s00454-002-2896-z","title":"The k Most Frequent Distances in the Plane","display_name":"The k Most Frequent Distances in the Plane","publication_year":2002,"publication_date":"2002-11-01","ids":{"openalex":"https://openalex.org/W2136361847","doi":"https://doi.org/10.1007/s00454-002-2896-z","mag":"2136361847"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-002-2896-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2896-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2896-z.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/s00454-002-2896-z.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020781039","display_name":"J\u00f3zsef Solymosi","orcid":"https://orcid.org/0000-0001-9181-0866"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Solymosi","raw_affiliation_strings":["Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA solymosi@math.ucsd.edu , USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA solymosi@math.ucsd.edu , USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031444562","display_name":"G\u00e1bor Tardos","orcid":"https://orcid.org/0000-0002-4281-1843"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Tardos","raw_affiliation_strings":["Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary tardos@renyi.hu , Hungary","Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary [email\u00a0protected], Hungary#TAB#"],"affiliations":[{"raw_affiliation_string":"Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary tardos@renyi.hu , Hungary","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary [email\u00a0protected], Hungary#TAB#","institution_ids":["https://openalex.org/I127817813"]}]},{"author_position":"last","author":{"id":null,"display_name":"T\u00f3th","orcid":null},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH","HU"],"is_corresponding":false,"raw_author_name":"T\u00f3th","raw_affiliation_strings":["Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary tardos@renyi.hu , Hungary","Institute for Theoretical Computer Science, ETH Zü;rich, CH-8092 Zü;rich, Switzerland toth@inf.ethz.ch, Switzerland#TAB#"],"affiliations":[{"raw_affiliation_string":"Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary tardos@renyi.hu , Hungary","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Institute for Theoretical Computer Science, ETH Zü;rich, CH-8092 Zü;rich, Switzerland toth@inf.ethz.ch, Switzerland#TAB#","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020781039"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.5921,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.84435146,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"28","issue":"4","first_page":"639","last_page":"648"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9957000017166138,"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":0.7584599256515503},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7371054887771606},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.7357534766197205},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6543731689453125},{"id":"https://openalex.org/keywords/concentric","display_name":"Concentric","score":0.5842987298965454},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.48301395773887634},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22579851746559143}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7584599256515503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7371054887771606},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.7357534766197205},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6543731689453125},{"id":"https://openalex.org/C90296322","wikidata":"https://www.wikidata.org/wiki/Q619776","display_name":"Concentric","level":2,"score":0.5842987298965454},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.48301395773887634},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22579851746559143}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-002-2896-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2896-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2896-z.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/s00454-002-2896-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2896-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2896-z.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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2136361847.pdf","grobid_xml":"https://content.openalex.org/works/W2136361847.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W13988344","https://openalex.org/W86126052","https://openalex.org/W1723997437","https://openalex.org/W1740201516","https://openalex.org/W1967390064","https://openalex.org/W2003689202","https://openalex.org/W2009870896","https://openalex.org/W2018858611","https://openalex.org/W2035775010","https://openalex.org/W2035884884","https://openalex.org/W2051635527","https://openalex.org/W2074709558","https://openalex.org/W2081260663","https://openalex.org/W2101764588","https://openalex.org/W2144898438","https://openalex.org/W2155681397","https://openalex.org/W2166961358","https://openalex.org/W2168138462","https://openalex.org/W2319149236","https://openalex.org/W2912202394","https://openalex.org/W4211205179"],"related_works":["https://openalex.org/W2032745795","https://openalex.org/W4241659117","https://openalex.org/W2042569643","https://openalex.org/W4252230788","https://openalex.org/W4235256213","https://openalex.org/W2254998354","https://openalex.org/W2061842045","https://openalex.org/W2586659751","https://openalex.org/W2549201271","https://openalex.org/W4252675521"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}