{"id":"https://openalex.org/W2026200800","doi":"https://doi.org/10.1016/0925-7721(95)00005-8","title":"Computing depth orders for fat objects and related problems","display_name":"Computing depth orders for fat objects and related problems","publication_year":1995,"publication_date":"1995-11-01","ids":{"openalex":"https://openalex.org/W2026200800","doi":"https://doi.org/10.1016/0925-7721(95)00005-8","mag":"2026200800"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00005-8","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/0925-7721(95)00005-8","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058649592","display_name":"Pankaj K. Agarwal","orcid":"https://orcid.org/0000-0002-9439-181X"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pankaj K. Agarwal","raw_affiliation_strings":["Department of Computer Science, Duke University Box 90129, Durham, NC 27708-0129, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Duke University Box 90129, Durham, NC 27708-0129, USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104278282","display_name":"Matthew J. Katz","orcid":null},"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":false,"raw_author_name":"Matthew J. Katz","raw_affiliation_strings":["Tel Aviv University, School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Ramat Aviv, 69978 Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"Tel Aviv University, School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Ramat Aviv, 69978 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/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"]},{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["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","Department of Computer Science, Duke University, Box 90129, Durham, NC 27708-0129, USA"],"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":"Department of Computer Science, Duke University, Box 90129, Durham, NC 27708-0129, USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2180,"currency":"USD","value_usd":2180,"provenance":"doaj"},"apc_paid":{"value":2180,"currency":"USD","value_usd":2180,"provenance":"doaj"},"fwci":3.306,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":51,"citation_normalized_percentile":{"value":0.881834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":92,"max":93},"biblio":{"volume":"5","issue":"4","first_page":"187","last_page":"206"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9999,"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":0.9999,"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":0.9915,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9877,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.519737}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.76345223},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6667744},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6661957},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.64458174},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.57040167},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.519737},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.50716376},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34290195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1319738},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00005-8","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/0925-7721(95)00005-8","pdf_url":null,"source":{"id":"https://openalex.org/S165542689","display_name":"Computational Geometry","issn_l":"0925-7721","issn":["0925-7721","1879-081X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":31,"referenced_works":["https://openalex.org/W1594991445","https://openalex.org/W2005314985","https://openalex.org/W2014732796","https://openalex.org/W2015425624","https://openalex.org/W2019176509","https://openalex.org/W2020590137","https://openalex.org/W2027190503","https://openalex.org/W2027387410","https://openalex.org/W2028430839","https://openalex.org/W2028747718","https://openalex.org/W2034181461","https://openalex.org/W2035836235","https://openalex.org/W2052333483","https://openalex.org/W2052755418","https://openalex.org/W2054011861","https://openalex.org/W2054236013","https://openalex.org/W2054459484","https://openalex.org/W2066150540","https://openalex.org/W2067695105","https://openalex.org/W2068141203","https://openalex.org/W2081192873","https://openalex.org/W2088617781","https://openalex.org/W2093241092","https://openalex.org/W2123869145","https://openalex.org/W2141110561","https://openalex.org/W2153204081","https://openalex.org/W2171758733","https://openalex.org/W2196955596","https://openalex.org/W2568603896","https://openalex.org/W3041834803","https://openalex.org/W3148691794"],"related_works":["https://openalex.org/W4288278856","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W3103304230","https://openalex.org/W3046727562","https://openalex.org/W2980963558","https://openalex.org/W2572370460","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W1882246857"],"abstract_inverted_index":{"Let":[0],"K":[1,28,35,37,43,69,86,96,127],"be":[2,88,129],"a":[3,20,48,71,82,98,116,123],"set":[4,72,99],"of":[5,14,24,62,73,100,141,146,149,152,162],"n":[6,74,101],"non-intersecting":[7],"objects":[8,26,105,153],"in":[9,27,90,131,154],"3-space.":[10],"A":[11],"depth":[12,53,83,124],"order":[13,22,84,125],"K,":[15,32,155],"if":[16,31],"it":[17,57],"exists,":[18],"is":[19,70,97,137,158],"linear":[21],"<":[23,44],"the":[25,138,144,147,159],"such":[29],"that":[30],"L":[33,41],"\u03f5":[34],"and":[36,55,103,111,156],"lies":[38],"vertically":[39],"below":[40],"then":[42,81,122],"L.":[45],"We":[46],"present":[47],"new":[49],"technique":[50],"for":[51,85,126],"computing":[52],"orders,":[54],"apply":[56],"to":[58],"several":[59],"special":[60],"classes":[61],"objects.":[63],"Our":[64],"results":[65],"include:":[66],"(i)":[67],"If":[68,95],"triangles":[75],"whose":[76,106],"xy-projections":[77,107,148],"are":[78,108,114],"all":[79,109],"\u2018fat\u2019,":[80],"can":[87,128],"computed":[89,130],"time":[91,132],"O(n":[92],"log5n).":[93],"(ii)":[94],"convex":[102],"simply-shaped":[104],"\u2018fat\u2019":[110],"their":[112],"sizes":[113],"within":[115],"constant":[117],"ratio":[118],"from":[119],"one":[120],"another,":[121],"O(n\u03bbs12(n)":[133],"log4n),":[134],"where":[135],"s":[136],"maximum":[139,160],"number":[140],"intersections":[142],"between":[143],"boundaries":[145],"any":[150],"pair":[151],"\u03bbs(n)":[157],"length":[161],"(n,s)":[163],"Davenport-Schinzel":[164],"sequences.":[165]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2026200800","counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2025-01-05T03:25:00.817324","created_date":"2016-06-24"}