{"id":"https://openalex.org/W4281707016","doi":"https://doi.org/10.1007/s00186-022-00788-8","title":"On the rectangular knapsack problem","display_name":"On the rectangular knapsack problem","publication_year":2022,"publication_date":"2022-06-09","ids":{"openalex":"https://openalex.org/W4281707016","doi":"https://doi.org/10.1007/s00186-022-00788-8"},"language":"en","primary_location":{"id":"doi:10.1007/s00186-022-00788-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-022-00788-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-022-00788-8.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00186-022-00788-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079504828","display_name":"Fritz B\u00f6kler","orcid":"https://orcid.org/0000-0002-7950-6965"},"institutions":[{"id":"https://openalex.org/I170658231","display_name":"Osnabr\u00fcck University","ror":"https://ror.org/04qmmjx98","country_code":"DE","type":"education","lineage":["https://openalex.org/I170658231"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Fritz B\u00f6kler","raw_affiliation_strings":["Department of Computer Science, Osnabr\u00fcck University, Osnabr\u00fcck, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7950-6965","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Osnabr\u00fcck University, Osnabr\u00fcck, Germany","institution_ids":["https://openalex.org/I170658231"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044475263","display_name":"Markus Chimani","orcid":"https://orcid.org/0000-0002-4681-5550"},"institutions":[{"id":"https://openalex.org/I170658231","display_name":"Osnabr\u00fcck University","ror":"https://ror.org/04qmmjx98","country_code":"DE","type":"education","lineage":["https://openalex.org/I170658231"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Chimani","raw_affiliation_strings":["Department of Computer Science, Osnabr\u00fcck University, Osnabr\u00fcck, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4681-5550","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Osnabr\u00fcck University, Osnabr\u00fcck, Germany","institution_ids":["https://openalex.org/I170658231"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003983903","display_name":"Mirko H. Wagner","orcid":"https://orcid.org/0000-0003-4593-8740"},"institutions":[{"id":"https://openalex.org/I170658231","display_name":"Osnabr\u00fcck University","ror":"https://ror.org/04qmmjx98","country_code":"DE","type":"education","lineage":["https://openalex.org/I170658231"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mirko H. Wagner","raw_affiliation_strings":["Department of Computer Science, Osnabr\u00fcck University, Osnabr\u00fcck, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4593-8740","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Osnabr\u00fcck University, Osnabr\u00fcck, Germany","institution_ids":["https://openalex.org/I170658231"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079504828"],"corresponding_institution_ids":["https://openalex.org/I170658231"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0804314,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"96","issue":"1","first_page":"149","last_page":"160"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9990000128746033,"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":0.9990000128746033,"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/T12288","display_name":"Optimization and Search Problems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/knapsack-problem","display_name":"Knapsack problem","score":0.9460139274597168},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.8120850324630737},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5318232178688049},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4692767858505249},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.46871131658554077},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4266064167022705},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42414969205856323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42290258407592773},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.1743292510509491}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.9460139274597168},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.8120850324630737},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5318232178688049},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4692767858505249},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.46871131658554077},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4266064167022705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42414969205856323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42290258407592773},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.1743292510509491},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00186-022-00788-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-022-00788-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-022-00788-8.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:mathme:v:96:y:2022:i:1:d:10.1007_s00186-022-00788-8","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00186-022-00788-8","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"},{"id":"pmh:oai:econstor.eu:10419/307079","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/307079","pdf_url":null,"source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"}],"best_oa_location":{"id":"doi:10.1007/s00186-022-00788-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00186-022-00788-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00186-022-00788-8.pdf","source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320329560","display_name":"Universit\u00e4t Osnabr\u00fcck","ror":"https://ror.org/04qmmjx98"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281707016.pdf","grobid_xml":"https://content.openalex.org/works/W4281707016.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2007458506","https://openalex.org/W2020203251","https://openalex.org/W2082782506","https://openalex.org/W2093067798","https://openalex.org/W2164056371","https://openalex.org/W2181448879","https://openalex.org/W2963081326","https://openalex.org/W3005919004","https://openalex.org/W3162269979"],"related_works":["https://openalex.org/W2978915811","https://openalex.org/W2956057537","https://openalex.org/W3005919004","https://openalex.org/W4386185430","https://openalex.org/W2974376984","https://openalex.org/W2273315864","https://openalex.org/W2787947809","https://openalex.org/W4319792305","https://openalex.org/W2031666601","https://openalex.org/W4281707016"],"abstract_inverted_index":{"Abstract":[0],"A":[1],"recent":[2],"paper":[3],"by":[4],"Schulze":[5],"et":[6],"al.":[7],"(Math":[8],"Methods":[9],"Oper":[10],"Res":[11],"92(1):107\u2013132,":[12],"2020)":[13],"presented":[14],"the":[15,27,30,72,96],"Rectangular":[16],"Knapsack":[17,33],"Problem":[18,34],"(":[19,35],"Rkp":[20,63,69,91,138],")":[21,136],"as":[22],"a":[23,58,66,110,114],"crucial":[24],"subproblem":[25],"in":[26,95,101],"study":[28],"on":[29],"Cardinality-constrained":[31],"Bi-objective":[32],"Cbkp":[36],").":[37],"To":[38],"this":[39,80],"end,":[40],"they":[41],"started":[42],"an":[43,54],"investigation":[44],"into":[45],"its":[46],"complexity":[47],"and":[48,65,105,113],"approximability.":[49],"The":[50],"key":[51],"results":[52],"are":[53],"-hardness":[55],"proof":[56],"for":[57,68,76,137],"more":[59,102],"general":[60],"scenario":[61],"than":[62],",":[64,70],"4.5-approximation":[67],"raising":[71],"question":[73],"of":[74],"improvements":[75],"either":[77],"result.":[78],"In":[79],"note":[81],"we":[82,87],"settle":[83],"both":[84,109],"questions":[85],"conclusively:":[86],"show":[88],"that":[89],"(a)":[90],"is":[92],"indeed":[93],"-hard":[94],"considered":[97],"setting":[98],"(and":[99],"even":[100],"restricted":[103],"settings),":[104],"(b)":[106],"there":[107],"exists":[108],"pseudopolynomial":[111],"algorithm":[112],"fully-polynomial":[115],"time":[116],"approximation":[117],"scheme":[118],"(i.e.,":[119],"efficient":[120],"approximability":[121],"within":[122],"any":[123],"desired":[124],"ratio":[125],"$$\\alpha":[126],"&gt;1$$":[127],"<mml:math":[128],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[129],"<mml:mrow>":[130],"<mml:mi>\u03b1</mml:mi>":[131],"<mml:mo>&gt;</mml:mo>":[132],"<mml:mn>1</mml:mn>":[133],"</mml:mrow>":[134],"</mml:math>":[135],".":[139]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
