{"id":"https://openalex.org/W2027913039","doi":"https://doi.org/10.1142/s021819591360008x","title":"FINDING THE LARGEST EMPTY DISK CONTAINING A QUERY POINT","display_name":"FINDING THE LARGEST EMPTY DISK CONTAINING A QUERY POINT","publication_year":2013,"publication_date":"2013-08-01","ids":{"openalex":"https://openalex.org/W2027913039","doi":"https://doi.org/10.1142/s021819591360008x","mag":"2027913039"},"language":"en","primary_location":{"id":"doi:10.1142/s021819591360008x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819591360008x","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006699796","display_name":"Haim Kaplan","orcid":"https://orcid.org/0000-0001-9586-8002"},"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"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"HAIM KAPLAN","raw_affiliation_strings":["School of Computer Science, Tel Aviv University, Tel Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"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"]},{"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":["IL","US"],"is_corresponding":false,"raw_author_name":"MICHA SHARIR","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA","School of Computer Science, Tel Aviv University, Tel Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"School of Computer Science, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006699796"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.14274583,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"04n05","first_page":"335","last_page":"355"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7204001545906067},{"id":"https://openalex.org/keywords/preprocessor","display_name":"Preprocessor","score":0.6569014191627502},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.6194220185279846},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6186877489089966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6157304644584656},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.596203088760376},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5687708854675293},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4328269362449646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3708431124687195},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32584118843078613},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29863977432250977},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.059808701276779175}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7204001545906067},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.6569014191627502},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.6194220185279846},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6186877489089966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6157304644584656},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.596203088760376},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5687708854675293},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4328269362449646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3708431124687195},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32584118843078613},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29863977432250977},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.059808701276779175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021819591360008x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021819591360008x","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Geometry &amp; Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1980092773","https://openalex.org/W1996036165","https://openalex.org/W1998909289","https://openalex.org/W2011297770","https://openalex.org/W2030839304","https://openalex.org/W2042800588","https://openalex.org/W2130596403","https://openalex.org/W2162639115","https://openalex.org/W3011379640","https://openalex.org/W3138865866"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W4256429076","https://openalex.org/W2012063272","https://openalex.org/W2348092930","https://openalex.org/W2138685729","https://openalex.org/W2371953206","https://openalex.org/W2361023359","https://openalex.org/W2349543044","https://openalex.org/W3007915326"],"abstract_inverted_index":{"Let":[0],"P":[1],"be":[2],"a":[3,22,64],"set":[4],"of":[5],"n":[6],"points":[7],"in":[8],"the":[9,31,48,55],"plane.":[10],"We":[11,72],"present":[12,74],"an":[13,75,79],"efficient":[14],"algorithm":[15],"for":[16,21],"preprocessing":[17,56,89],"P,":[18],"so":[19],"that,":[20],"given":[23],"query":[24,65,81],"point":[25],"q,":[26],"we":[27],"can":[28],"quickly":[29],"report":[30],"largest":[32],"disk":[33],"that":[34],"contains":[35],"q":[36],"but":[37],"its":[38],"interior":[39],"is":[40,51,58],"disjoint":[41],"from":[42],"P.":[43],"The":[44],"storage":[45,87],"required":[46],"by":[47],"data":[49],"structure":[50],"O(n":[52,59],"log":[53,60,68],"n),":[54,62],"cost":[57,82],"2":[61,69],"and":[63,83,88],"takes":[66],"O(":[67],"n)":[70],"time.":[71],"also":[73],"alternative":[76],"solution":[77],"with":[78,84],"improved":[80],"slightly":[85],"worse":[86],"requirements.":[90]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
