{"id":"https://openalex.org/W3021361695","doi":"https://doi.org/10.1080/00207543.2020.1755471","title":"Sparsest packing of two-dimensional objects","display_name":"Sparsest packing of two-dimensional objects","publication_year":2020,"publication_date":"2020-05-04","ids":{"openalex":"https://openalex.org/W3021361695","doi":"https://doi.org/10.1080/00207543.2020.1755471","mag":"3021361695"},"language":"en","primary_location":{"id":"doi:10.1080/00207543.2020.1755471","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207543.2020.1755471","pdf_url":null,"source":{"id":"https://openalex.org/S65690446","display_name":"International Journal of Production Research","issn_l":"0020-7543","issn":["0020-7543","1366-588X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Production Research","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/A5046333519","display_name":"\u0422. Romanova","orcid":"https://orcid.org/0000-0002-8618-4917"},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I4210121111","display_name":"Anatolii Pidhornyi Institute of Power Machines and Systems","ror":"https://ror.org/02ezqbp79","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210121111"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Tatiana Romanova","raw_affiliation_strings":["Department of Mathematical Modeling and Optimal Design, A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-8618-4917","affiliations":[{"raw_affiliation_string":"Department of Mathematical Modeling and Optimal Design, A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine","institution_ids":["https://openalex.org/I4210121111","https://openalex.org/I149851306"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102955299","display_name":"Alexander Pankratov","orcid":"https://orcid.org/0000-0002-2958-8923"},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I4210121111","display_name":"Anatolii Pidhornyi Institute of Power Machines and Systems","ror":"https://ror.org/02ezqbp79","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210121111"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Alexander Pankratov","raw_affiliation_strings":["Department of Mathematical Modeling and Optimal Design, A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-2958-8923","affiliations":[{"raw_affiliation_string":"Department of Mathematical Modeling and Optimal Design, A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine","institution_ids":["https://openalex.org/I4210121111","https://openalex.org/I149851306"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088187330","display_name":"Igor Litvinchev","orcid":"https://orcid.org/0000-0002-1850-4755"},"institutions":[{"id":"https://openalex.org/I169046204","display_name":"Universidad Aut\u00f3noma de Nuevo Le\u00f3n","ror":"https://ror.org/01fh86n78","country_code":"MX","type":"education","lineage":["https://openalex.org/I169046204"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Igor Litvinchev","raw_affiliation_strings":["Faculty of Mechanical and Electrical Engineering, Nuevo Leon State University, San Nicolas de los Garza, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-1850-4755","affiliations":[{"raw_affiliation_string":"Faculty of Mechanical and Electrical Engineering, Nuevo Leon State University, San Nicolas de los Garza, Mexico","institution_ids":["https://openalex.org/I169046204"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035322903","display_name":"Sergiy Plankovskyy","orcid":"https://orcid.org/0000-0003-2908-903X"},"institutions":[{"id":"https://openalex.org/I23686167","display_name":"National Aerospace University \u2013 Kharkiv Aviation Institute","ror":"https://ror.org/048j5n646","country_code":"UA","type":"education","lineage":["https://openalex.org/I23686167"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Sergiy Plankovskyy","raw_affiliation_strings":["Department of Aircraft Manufacturing Technology, National Aerospace University \u201cKharkiv Aviation Institute\u201d, Kharkiv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0003-2908-903X","affiliations":[{"raw_affiliation_string":"Department of Aircraft Manufacturing Technology, National Aerospace University \u201cKharkiv Aviation Institute\u201d, Kharkiv, Ukraine","institution_ids":["https://openalex.org/I23686167"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001775618","display_name":"Yevgen Tsegelnyk","orcid":"https://orcid.org/0000-0003-1261-9890"},"institutions":[{"id":"https://openalex.org/I23686167","display_name":"National Aerospace University \u2013 Kharkiv Aviation Institute","ror":"https://ror.org/048j5n646","country_code":"UA","type":"education","lineage":["https://openalex.org/I23686167"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Yevgen Tsegelnyk","raw_affiliation_strings":["Department of Aircraft Manufacturing Technology, National Aerospace University \u201cKharkiv Aviation Institute\u201d, Kharkiv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0003-1261-9890","affiliations":[{"raw_affiliation_string":"Department of Aircraft Manufacturing Technology, National Aerospace University \u201cKharkiv Aviation Institute\u201d, Kharkiv, Ukraine","institution_ids":["https://openalex.org/I23686167"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050785465","display_name":"Olga Shypul","orcid":"https://orcid.org/0000-0002-1356-5831"},"institutions":[{"id":"https://openalex.org/I23686167","display_name":"National Aerospace University \u2013 Kharkiv Aviation Institute","ror":"https://ror.org/048j5n646","country_code":"UA","type":"education","lineage":["https://openalex.org/I23686167"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Olga Shypul","raw_affiliation_strings":["Department of Aircraft Manufacturing Technology, National Aerospace University \u201cKharkiv Aviation Institute\u201d, Kharkiv, Ukraine"],"raw_orcid":"https://orcid.org/0000-0002-1356-5831","affiliations":[{"raw_affiliation_string":"Department of Aircraft Manufacturing Technology, National Aerospace University \u201cKharkiv Aviation Institute\u201d, Kharkiv, Ukraine","institution_ids":["https://openalex.org/I23686167"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5046333519"],"corresponding_institution_ids":["https://openalex.org/I149851306","https://openalex.org/I4210121111"],"apc_list":null,"apc_paid":null,"fwci":3.0732,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.92163872,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"59","issue":"13","first_page":"3900","last_page":"3915"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.998199999332428,"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/T12176","display_name":"Optimization and Packing Problems","score":0.998199999332428,"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/T11814","display_name":"Advanced Manufacturing and Logistics Optimization","score":0.9959999918937683,"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/T10783","display_name":"Additive Manufacturing and 3D Printing Technologies","score":0.991599977016449,"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/packing-problems","display_name":"Packing problems","score":0.8263472318649292},{"id":"https://openalex.org/keywords/container","display_name":"Container (type theory)","score":0.7864971160888672},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6017361879348755},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.596687912940979},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5716232061386108},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.5395308136940002},{"id":"https://openalex.org/keywords/bin-packing-problem","display_name":"Bin packing problem","score":0.4814574122428894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4660782516002655},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4535452425479889},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3797312378883362},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32282698154449463},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3219344913959503},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1985197365283966},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1934172809123993}],"concepts":[{"id":"https://openalex.org/C130253271","wikidata":"https://www.wikidata.org/wiki/Q3851477","display_name":"Packing problems","level":2,"score":0.8263472318649292},{"id":"https://openalex.org/C2781018962","wikidata":"https://www.wikidata.org/wiki/Q5164884","display_name":"Container (type theory)","level":2,"score":0.7864971160888672},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6017361879348755},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.596687912940979},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5716232061386108},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.5395308136940002},{"id":"https://openalex.org/C87219788","wikidata":"https://www.wikidata.org/wiki/Q814581","display_name":"Bin packing problem","level":3,"score":0.4814574122428894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4660782516002655},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4535452425479889},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3797312378883362},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32282698154449463},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3219344913959503},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1985197365283966},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1934172809123993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C156273044","wikidata":"https://www.wikidata.org/wiki/Q4913766","display_name":"Bin","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207543.2020.1755471","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207543.2020.1755471","pdf_url":null,"source":{"id":"https://openalex.org/S65690446","display_name":"International Journal of Production Research","issn_l":"0020-7543","issn":["0020-7543","1366-588X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Production Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:taf:tprsxx:v:59:y:2021:i:13:p:3900-3915","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1080/00207543.2020.1755471","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W29007683","https://openalex.org/W231891190","https://openalex.org/W1566796596","https://openalex.org/W1923527284","https://openalex.org/W1974255097","https://openalex.org/W1979411905","https://openalex.org/W2000914712","https://openalex.org/W2039355562","https://openalex.org/W2043069749","https://openalex.org/W2048802156","https://openalex.org/W2050024620","https://openalex.org/W2051628631","https://openalex.org/W2058783655","https://openalex.org/W2123871098","https://openalex.org/W2178154271","https://openalex.org/W2199861121","https://openalex.org/W2218130416","https://openalex.org/W2240053161","https://openalex.org/W2259068132","https://openalex.org/W2280720710","https://openalex.org/W2344325901","https://openalex.org/W2562820959","https://openalex.org/W2567786109","https://openalex.org/W2584429941","https://openalex.org/W2585759288","https://openalex.org/W2591084903","https://openalex.org/W2788182033","https://openalex.org/W2789444712","https://openalex.org/W2794343818","https://openalex.org/W2892425242","https://openalex.org/W2897022983","https://openalex.org/W2902875270","https://openalex.org/W2903769548","https://openalex.org/W2933260104","https://openalex.org/W2939892897","https://openalex.org/W2942236584","https://openalex.org/W2942947084","https://openalex.org/W2944379335","https://openalex.org/W2954579693","https://openalex.org/W2970958795","https://openalex.org/W2976164422","https://openalex.org/W2981834501","https://openalex.org/W2985267851","https://openalex.org/W2987033796","https://openalex.org/W2992743759","https://openalex.org/W2996971298"],"related_works":["https://openalex.org/W2078833192","https://openalex.org/W2042249499","https://openalex.org/W2398075730","https://openalex.org/W2117588054","https://openalex.org/W2351297228","https://openalex.org/W2087826159","https://openalex.org/W2171213122","https://openalex.org/W1442399089","https://openalex.org/W4234742569","https://openalex.org/W2598380049"],"abstract_inverted_index":{"The":[0,11,72,88],"concept":[1],"of":[2,45,75],"the":[3,18,21,29,34,40,43,46,103,131],"sparsest":[4,12,73],"packing":[5,13,74],"is":[6,14,48,54,82,109,117,122],"introduced":[7],"in":[8,20,78],"this":[9],"paper.":[10],"aimed":[15],"to":[16,85,129],"place":[17],"objects":[19,41,77,89],"container":[22,47,81],"as":[23,25,36,63],"distant":[24],"possible.":[26],"More":[27],"specifically,":[28],"minimal":[30],"Euclidean":[31],"distance":[32],"between":[33,39],"objects,":[35],"well":[37],"as,":[38],"and":[42,59,66,99,111,124],"boundary":[44],"maximised.":[49],"This":[50],"new":[51],"problem":[52,116],"statement":[53],"motivated":[55],"by":[56,68,97],"modern":[57],"clean":[58],"energy-saving":[60],"technologies":[61],"such":[62],"ultrasonic":[64],"hardening":[65],"finishing":[67],"detonating":[69],"gas":[70],"mixtures.":[71],"two-dimensional":[76],"a":[79,106,112],"circular":[80],"considered":[83],"subject":[84],"balancing":[86],"conditions.":[87],"may":[90],"have":[91],"regular":[92],"or":[93],"irregular":[94],"shapes":[95],"bounded":[96],"arcs":[98],"line":[100],"segments.":[101],"Using":[102],"phi-function":[104],"technique":[105],"mathematical":[107],"model":[108],"formulated":[110],"corresponding":[113],"nonlinear":[114],"programming":[115],"stated.":[118],"A":[119],"solution":[120],"algorithm":[121],"proposed":[123],"computational":[125],"results":[126],"are":[127],"presented":[128],"illustrate":[130],"approach.":[132]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}