{"id":"https://openalex.org/W1919151996","doi":"https://doi.org/10.37236/2681","title":"On the Union Complexity of Diametral Disks","display_name":"On the Union Complexity of Diametral Disks","publication_year":2013,"publication_date":"2013-06-07","ids":{"openalex":"https://openalex.org/W1919151996","doi":"https://doi.org/10.37236/2681","mag":"1919151996"},"language":"en","primary_location":{"id":"doi:10.37236/2681","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2681","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p53/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p53/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042232059","display_name":"Boris Aronov","orcid":"https://orcid.org/0000-0003-3110-4702"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Boris Aronov","raw_affiliation_strings":["Polytechnic Institute of NYU","Polytechnic Institute of NYU#TAB#"],"affiliations":[{"raw_affiliation_string":"Polytechnic Institute of NYU","institution_ids":["https://openalex.org/I90965887"]},{"raw_affiliation_string":"Polytechnic Institute of NYU#TAB#","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062579777","display_name":"Muriel Dulieu","orcid":null},"institutions":[{"id":"https://openalex.org/I90965887","display_name":"SUNY Polytechnic Institute","ror":"https://ror.org/000fxgx19","country_code":"US","type":"education","lineage":["https://openalex.org/I90965887"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Muriel Dulieu","raw_affiliation_strings":["Polytechnic Institute of NYU","Polytechnic Institute of NYU#TAB#"],"affiliations":[{"raw_affiliation_string":"Polytechnic Institute of NYU","institution_ids":["https://openalex.org/I90965887"]},{"raw_affiliation_string":"Polytechnic Institute of NYU#TAB#","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085876020","display_name":"Rom Pinchasi","orcid":"https://orcid.org/0000-0002-1604-6877"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Rom Pinchasi","raw_affiliation_strings":["Technion"],"affiliations":[{"raw_affiliation_string":"Technion","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055296785","display_name":"Micha Sharir","orcid":"https://orcid.org/0000-0002-2541-3763"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["IL","US"],"is_corresponding":false,"raw_author_name":"Micha Sharir","raw_affiliation_strings":["Tel Aviv University and Courant Institute of Mathematical Sciences"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University and Courant Institute of Mathematical Sciences","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042232059"],"corresponding_institution_ids":["https://openalex.org/I57206974","https://openalex.org/I90965887"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.0992521,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"20","issue":"2","first_page":null,"last_page":null},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9993000030517578,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/combinatorics","display_name":"Combinatorics","score":0.8431100845336914},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8320736885070801},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6778762340545654},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6568971276283264},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6444753408432007},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.6129250526428223},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5340251922607422},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4971778690814972},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.45255860686302185},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23468217253684998},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1063028872013092},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08801022171974182}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8431100845336914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8320736885070801},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6778762340545654},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6568971276283264},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6444753408432007},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.6129250526428223},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5340251922607422},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4971778690814972},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.45255860686302185},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23468217253684998},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1063028872013092},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08801022171974182},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/2681","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2681","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p53/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.298.9780","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.9780","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~michas/ddiamx.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/2681","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2681","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p53/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1227625532","display_name":null,"funder_award_id":"CCF-08-30272","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1395944067","display_name":"Computional Physics: Structural, Electronic and Optical Properties of Materials","funder_award_id":"30272","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G1699706384","display_name":null,"funder_award_id":"I-CORE","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G3760795155","display_name":null,"funder_award_id":"1357/12","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G5328706984","display_name":"Etude de m\u00e9thodes avanc\u00e9es d'apprentissage auto- matique.","funder_award_id":"20082","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G7315415636","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G7965623349","display_name":null,"funder_award_id":"Center No. 4/11","funder_id":"https://openalex.org/F4320335016","funder_display_name":"Israeli Centers for Research Excellence"},{"id":"https://openalex.org/G8291921620","display_name":null,"funder_award_id":"338/09","funder_id":"https://openalex.org/F4320335016","funder_display_name":"Israeli Centers for Research Excellence"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320322596","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49"},{"id":"https://openalex.org/F4320335016","display_name":"Israeli Centers for Research Excellence","ror":"https://ror.org/03w2v9593"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1919151996.pdf","grobid_xml":"https://content.openalex.org/works/W1919151996.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W179323378","https://openalex.org/W1444168583","https://openalex.org/W1980092773","https://openalex.org/W2007311757","https://openalex.org/W2022266599","https://openalex.org/W2025410851","https://openalex.org/W2141696749","https://openalex.org/W4300640952"],"related_works":["https://openalex.org/W4297976568","https://openalex.org/W2962851451","https://openalex.org/W2165434229","https://openalex.org/W2895641489","https://openalex.org/W3098813812","https://openalex.org/W2949921337","https://openalex.org/W1879246310","https://openalex.org/W4288090900","https://openalex.org/W2049395806","https://openalex.org/W4311900556"],"abstract_inverted_index":{"Let":[0],"$S$":[1,27,57],"be":[2,14],"a":[3,22,29,46],"set":[4,17],"of":[5,18,24,26,37,40,56],"$n$":[6],"points":[7,25,55],"in":[8,59],"the":[9,34,38,54,62],"plane,":[10],"and":[11,44],"let":[12],"$\\mathcal{D}$":[13,41],"an":[15],"arbitrary":[16],"disks,":[19],"each":[20],"having":[21],"pair":[23],"as":[28],"diameter.":[30],"We":[31],"show":[32],"that":[33],"combinatorial":[35],"complexity":[36],"union":[39],"is":[42],"$O(n^{3/2})$,":[43],"provide":[45],"lower":[47],"bound":[48,64],"construction":[49],"with":[50],"$\\Omega(n^{4/3})$":[51],"complexity.":[52],"If":[53],"are":[58],"convex":[60],"position,":[61],"upper":[63],"drops":[65],"to":[66],"$O(n\\log":[67],"n)$.":[68]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}