{"id":"https://openalex.org/W2100387058","doi":"https://doi.org/10.1142/s0218195996000125","title":"MAXIMAL EMPTY ELLIPSOIDS","display_name":"MAXIMAL EMPTY ELLIPSOIDS","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W2100387058","doi":"https://doi.org/10.1142/s0218195996000125","mag":"2100387058"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195996000125","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195996000125","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/A5055035145","display_name":"Rex A. Dwyer","orcid":null},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"REX A. DWYER","raw_affiliation_strings":["Computer Science Department, North Carolina State University, Raleigh, NC 27695\u20138206, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, North Carolina State University, Raleigh, NC 27695\u20138206, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108809344","display_name":"William F. Eddy","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"WILLIAM F. EDDY","raw_affiliation_strings":["Statistics Department, Carnegie-Mellon University, Pittsburgh, PA 15213, USA","Statistics Department, Carnegie Mellon University, Pittsburgh, PA 15213 USA,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Statistics Department, Carnegie-Mellon University, Pittsburgh, PA 15213, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Statistics Department, Carnegie Mellon University, Pittsburgh, PA 15213 USA,","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0827,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.80020719,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"06","issue":"02","first_page":"169","last_page":"185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9878000020980835,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9829000234603882,"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/T11904","display_name":"Spatial Cognition and Navigation","score":0.9702000021934509,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.8748542070388794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.805404782295227},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6863776445388794},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6388715505599976},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5844340324401855},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.5246360898017883},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5058783888816833},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4834914803504944},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.4505765736103058},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.44478118419647217},{"id":"https://openalex.org/keywords/task","display_name":"Task (project management)","score":0.4247044026851654},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1208362877368927},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05129575729370117}],"concepts":[{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.8748542070388794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.805404782295227},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6863776445388794},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6388715505599976},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5844340324401855},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.5246360898017883},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5058783888816833},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4834914803504944},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4505765736103058},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.44478118419647217},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.4247044026851654},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1208362877368927},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05129575729370117},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195996000125","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195996000125","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":[{"display_name":"Sustainable cities and communities","score":0.8199999928474426,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2390718407","https://openalex.org/W2005485125","https://openalex.org/W2085363807","https://openalex.org/W2034124193","https://openalex.org/W2379017606","https://openalex.org/W2156319555","https://openalex.org/W2941765012","https://openalex.org/W2171970890","https://openalex.org/W2356423988","https://openalex.org/W4308273173"],"abstract_inverted_index":{"The":[0,75],"task":[1],"of":[2,12,32,36,91],"finding":[3],"the":[4,30,33,37,51,78,87,92],"largest":[5],"empty":[6],"ellipsoid":[7,93],"defined":[8],"by":[9,28,82],"a":[10,41],"set":[11],"n":[13,71],"point":[14],"sites":[15,38],"in":[16,43,50],"Rd":[17],"is":[18,21,48,55,68],"investigated.":[19],"It":[20],"shown":[22],"that":[23,57],"this":[24],"can":[25],"be":[26],"solved":[27],"enumerating":[29],"facets":[31],"convex":[34],"hull":[35],"projected":[39],"onto":[40],"manifold":[42],"R[d(d+3)/2].":[44],"While":[45],"O(n[d(d+3)/4])":[46],"time":[47,80],"required":[49],"worst":[52],"case,":[53],"it":[54],"found":[56],"O(nd)":[58],"suffices":[59],"on":[60,77,86],"average":[61],"for":[62],"independent":[63],"uniform":[64],"points":[65],"when":[66],"d":[67],"fixed":[69],"and":[70,89,101],"increases":[72],"without":[73],"bound.":[74],"effects":[76],"running":[79],"caused":[81],"imposing":[83],"certain":[84],"restrictions":[85],"orientation":[88],"shape":[90],"are":[94,104],"also":[95],"described.":[96],"Applications":[97],"to":[98],"motion":[99],"planning":[100],"design":[102],"centering":[103],"considered":[105],"briefly.":[106]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
