{"id":"https://openalex.org/W2123260089","doi":"https://doi.org/10.1142/s0218195998000175","title":"Decision Trees for Geometric Models","display_name":"Decision Trees for Geometric Models","publication_year":1998,"publication_date":"1998-06-01","ids":{"openalex":"https://openalex.org/W2123260089","doi":"https://doi.org/10.1142/s0218195998000175","mag":"2123260089"},"language":"en","primary_location":{"id":"doi:10.1142/s0218195998000175","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195998000175","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/A5037943415","display_name":"Esther M. Arkin","orcid":"https://orcid.org/0009-0005-8542-931X"},"institutions":[{"id":"https://openalex.org/I1327163397","display_name":"State University of New York","ror":"https://ror.org/01q1z8k08","country_code":"US","type":"education","lineage":["https://openalex.org/I1327163397"]},{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Esther M. Arkin","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, USA","institution_ids":["https://openalex.org/I1327163397","https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045375742","display_name":"Henk Meijer","orcid":"https://orcid.org/0000-0003-0406-3327"},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Henk Meijer","raw_affiliation_strings":["Department of Computer and Information Science, Queen's University, Kingston, Ontario, K7L 3N6, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science, Queen's University, Kingston, Ontario, K7L 3N6, Canada","institution_ids":["https://openalex.org/I204722609"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015247956","display_name":"Joseph S. B. Mitchell","orcid":"https://orcid.org/0000-0002-0152-2279"},"institutions":[{"id":"https://openalex.org/I1327163397","display_name":"State University of New York","ror":"https://ror.org/01q1z8k08","country_code":"US","type":"education","lineage":["https://openalex.org/I1327163397"]},{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joseph S. B. Mitchell","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, Stony Brook, NY 11794-3600, USA","institution_ids":["https://openalex.org/I1327163397","https://openalex.org/I59553526"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112711900","display_name":"David Rappaport","orcid":null},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"David Rappaport","raw_affiliation_strings":["Department of Computer and Information Science, Queen's University, Kingston, Ontario, K7L 3N6, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer and Information Science, Queen's University, Kingston, Ontario, K7L 3N6, Canada","institution_ids":["https://openalex.org/I204722609"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060741187","display_name":"Steven Skiena","orcid":"https://orcid.org/0000-0003-0397-7514"},"institutions":[{"id":"https://openalex.org/I1327163397","display_name":"State University of New York","ror":"https://ror.org/01q1z8k08","country_code":"US","type":"education","lineage":["https://openalex.org/I1327163397"]},{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven S. Skiena","raw_affiliation_strings":["Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY 11794-4400, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY 11794-4400, USA","institution_ids":["https://openalex.org/I1327163397","https://openalex.org/I59553526"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9365,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.78067576,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"08","issue":"03","first_page":"343","last_page":"363"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9969000220298767,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.9941999912261963,"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/mathematics","display_name":"Mathematics","score":0.6827937364578247},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6221004128456116},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5258291959762573},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5098008513450623},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5006945133209229},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.49752381443977356},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4637295603752136},{"id":"https://openalex.org/keywords/interval-tree","display_name":"Interval tree","score":0.4399343729019165},{"id":"https://openalex.org/keywords/decision-problem","display_name":"Decision problem","score":0.4343242347240448},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43247413635253906},{"id":"https://openalex.org/keywords/decision-tree","display_name":"Decision tree","score":0.42869627475738525},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.41851890087127686},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.4155755043029785},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3989325165748596},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3716523051261902},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.30378204584121704},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29152345657348633},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.24585884809494019},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2241896390914917},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09288656711578369}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6827937364578247},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6221004128456116},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5258291959762573},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5098008513450623},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5006945133209229},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.49752381443977356},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4637295603752136},{"id":"https://openalex.org/C84927040","wikidata":"https://www.wikidata.org/wiki/Q6057306","display_name":"Interval tree","level":4,"score":0.4399343729019165},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.4343242347240448},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43247413635253906},{"id":"https://openalex.org/C84525736","wikidata":"https://www.wikidata.org/wiki/Q831366","display_name":"Decision tree","level":2,"score":0.42869627475738525},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.41851890087127686},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.4155755043029785},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3989325165748596},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3716523051261902},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.30378204584121704},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29152345657348633},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.24585884809494019},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2241896390914917},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09288656711578369},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218195998000175","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195998000175","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":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6800000071525574}],"awards":[],"funders":[{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1970074386","https://openalex.org/W1985642978","https://openalex.org/W1995282992","https://openalex.org/W2003525146","https://openalex.org/W2010788277","https://openalex.org/W2013451793","https://openalex.org/W2015696135","https://openalex.org/W2022671649","https://openalex.org/W2024262734","https://openalex.org/W2026311529","https://openalex.org/W2040924621","https://openalex.org/W2061734820","https://openalex.org/W2066577300","https://openalex.org/W2068204893","https://openalex.org/W2076107933","https://openalex.org/W2080209778","https://openalex.org/W2085041675","https://openalex.org/W2088549534","https://openalex.org/W2091897099","https://openalex.org/W2133431834","https://openalex.org/W2147030301","https://openalex.org/W2153050879","https://openalex.org/W4210890186"],"related_works":["https://openalex.org/W2107381954","https://openalex.org/W2117536196","https://openalex.org/W3022865202","https://openalex.org/W2113320216","https://openalex.org/W2906792929","https://openalex.org/W1510719821","https://openalex.org/W2074513192","https://openalex.org/W2382364329","https://openalex.org/W2022598760","https://openalex.org/W2372574250"],"abstract_inverted_index":{"A":[0],"fundamental":[1],"problem":[2,48],"in":[3,21,139,170],"model-based":[4],"computer":[5],"vision":[6],"is":[7,19,39,78,150,158,181],"that":[8,31,82,144,188],"of":[9,12,16,49,66,116,137,154,189],"identifying":[10],"which":[11,75],"a":[13,25,37,42,83,113,135,146,176],"given":[14,43,133],"set":[15,136],"geometric":[17],"models":[18,96,131],"present":[20,40],"an":[22,29,57,121,162,190],"image.":[23],"Considering":[24],"\"probe\"":[26],"to":[27,62,73],"be":[28],"oracle":[30],"tells":[32],"us":[33],"whether":[34],"or":[35],"not":[36,106],"model":[38,77],"at":[41,182],"point,":[44],"we":[45,119,194],"study":[46],"the":[47,60,64,70,130,140,155,171],"computing":[50],"efficient":[51,122,163],"strategies":[52],"(\"decision":[53],"trees\")":[54],"for":[55,93,124,203],"probing":[56],"image,":[58],"with":[59],"goal":[61],"minimize":[63],"number":[65],"probes":[67],"necessary":[68],"(in":[69,97],"worst":[71],"case)":[72],"determine":[74],"single":[76],"present.":[79],"We":[80,142,160],"show":[81,143,168],"\u2308l":[84,184],"g":[85,185],"k\u2309":[86,186],"height":[87,148,180],"binary":[88],"decision":[89,127,177],"tree":[90,149,178],"always":[91],"exists":[92],"k":[94],"polygonal":[95],"fixed":[98],"position),":[99],"provided":[100],"(1)":[101],"they":[102,111],"are":[103,132],"non-degenerate":[104],"(do":[105],"share":[107,112],"boundaries)":[108],"and":[109,167],"(2)":[110],"common":[114],"point":[115],"intersection.":[117],"Further,":[118],"give":[120],"algorithm":[123],"constructing":[125,145],"such":[126],"tress":[128],"when":[129],"as":[134],"polygons":[138],"plane.":[141],"minimum":[147],"NP-complete":[151],"if":[152],"either":[153],"two":[156],"assumptions":[157],"omitted.":[159],"provide":[161],"greedy":[164],"heuristic":[165],"strategy":[166],"that,":[169],"general":[172],"case,":[173],"it":[174],"yields":[175],"whose":[179,199],"most":[183],"times":[187],"optimal":[191],"tree.":[192],"Finally,":[193],"discuss":[195],"some":[196],"restricted":[197],"cases":[198],"special":[200],"structure":[201],"allows":[202],"improved":[204],"results.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
