{"id":"https://openalex.org/W7140880190","doi":"https://doi.org/10.48550/arxiv.2603.23970","title":"Approximation Schemes and Structural Barriers for the Two-Dimensional Knapsack Problem with Rotations","display_name":"Approximation Schemes and Structural Barriers for the Two-Dimensional Knapsack Problem with Rotations","publication_year":2026,"publication_date":"2026-03-25","ids":{"openalex":"https://openalex.org/W7140880190","doi":"https://doi.org/10.48550/arxiv.2603.23970"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.23970","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23970","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.23970","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072552073","display_name":"Debajyoti Kar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kar, Debajyoti","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085907661","display_name":"Arindam Khan","orcid":"https://orcid.org/0000-0001-7505-1687"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Khan, Arindam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067503013","display_name":"Andreas Wiese","orcid":"https://orcid.org/0000-0003-3705-016X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wiese, Andreas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9610000252723694,"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":0.9610000252723694,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.019099999219179153,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.0031999999191612005,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.9121000170707703},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.7674999833106995},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.6187999844551086},{"id":"https://openalex.org/keywords/polynomial-time-approximation-scheme","display_name":"Polynomial-time approximation scheme","score":0.5501999855041504},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4465999901294708},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4447000026702881},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4311999976634979},{"id":"https://openalex.org/keywords/continuous-knapsack-problem","display_name":"Continuous knapsack problem","score":0.37369999289512634}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.9121000170707703},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7674999833106995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7479000091552734},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6187999844551086},{"id":"https://openalex.org/C99140742","wikidata":"https://www.wikidata.org/wiki/Q843550","display_name":"Polynomial-time approximation scheme","level":3,"score":0.5501999855041504},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5472000241279602},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4311999976634979},{"id":"https://openalex.org/C94569963","wikidata":"https://www.wikidata.org/wiki/Q5165487","display_name":"Continuous knapsack problem","level":3,"score":0.37369999289512634},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.373199999332428},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3668999969959259},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3447999954223633},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3402999937534332},{"id":"https://openalex.org/C130253271","wikidata":"https://www.wikidata.org/wiki/Q3851477","display_name":"Packing problems","level":2,"score":0.335099995136261},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3224000036716461},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2854999899864197},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.2709999978542328},{"id":"https://openalex.org/C134516590","wikidata":"https://www.wikidata.org/wiki/Q475603","display_name":"Set packing","level":3,"score":0.26579999923706055},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.23970","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23970","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.23970","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.23970","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,60,78,94,98,108,117,135,143,188,225,232,237,255,272,276],"two-dimensional":[3],"(geometric)":[4],"knapsack":[5,17],"problem":[6,61,264],"with":[7,23,72,265],"rotations":[8,268],"(2DKR),":[9],"in":[10,43,77,97,107,116,154,224,271],"which":[11,155,179],"we":[12,130,147,192,212,247],"are":[13,151,158],"given":[14],"a":[15,19,31,91,103,132,162,174,205,219,249],"square":[16],"and":[18,217],"set":[20],"of":[21,35,66,110,138,165,182,198,252,258],"rectangles":[22,36,51],"associated":[24],"profits.":[25],"The":[26,54],"objective":[27],"is":[28,171,200],"to":[29,75,82,142,203,243],"find":[30],"maximum":[32],"profit":[33],"subset":[34],"that":[37,149,194],"can":[38],"be":[39,181],"packed":[40,159],"without":[41,145,241,267],"overlap":[42],"an":[44,63,73],"axis-aligned":[45],"manner,":[46],"possibly":[47],"by":[48,52,119],"rotating":[49],"some":[50],"$90^{\\circ}$.":[53],"best-known":[55,233],"polynomial":[56],"time":[57,257],"algorithm":[58,221,261],"for":[59,68,93,134,187,222,236,262],"has":[62,101],"approximation":[64,207,234],"ratio":[65,208,235],"$3/2+\u03b5$":[67],"any":[69,259],"constant":[70,163],"$\u03b5&gt;0$,":[71],"improvement":[74],"$4/3+\u03b5$":[76],"cardinality":[79,99,136,273],"case,":[80,100,191],"due":[81],"G{\u00e1}lvez":[83],"et":[84,121],"al.":[85,122],"(FOCS":[86],"2017,":[87],"TALG":[88],"2021).":[89],"Obtaining":[90],"PTAS":[92,133],"problem,":[95],"even":[96,270],"remained":[102],"major":[104],"open":[105],"question":[106],"setting":[109,144],"multidimensional":[111],"packing":[112,199],"problems,":[113],"as":[114],"mentioned":[115],"survey":[118],"Christensen":[120],"(Computer":[123],"Science":[124],"Review,":[125],"2017).":[126],"In":[127,140,185],"this":[128,195,214],"paper,":[129],"present":[131],"case":[137,239],"2DKR.":[139],"contrast":[141],"rotations,":[146],"show":[148],"there":[150],"$(1+\u03b5)$-approximate":[152],"solutions":[153],"all":[156],"items":[157],"greedily":[160],"inside":[161],"number":[164],"rectangular":[166],"{\\em":[167,240],"containers}.":[168],"Our":[169,228],"result":[170],"based":[172],"on":[173,254],"new":[175],"resource":[176],"contraction":[177],"lemma,":[178],"might":[180],"independent":[183],"interest.":[184],"contrast,":[186],"general":[189],"weighted":[190,226],"prove":[193],"simple":[196],"type":[197],"not":[201],"sufficient":[202],"obtain":[204],"better":[206],"than":[209],"$1.5$.":[210],"However,":[211],"break":[213],"structural":[215],"barrier":[216],"design":[218],"$(1.497+\u03b5)$-approximation":[220],"2DKR":[223],"case.":[227],"arguments":[229],"also":[230],"improve":[231],"(weighted)":[238],"rotations}":[242],"$13/7+\u03b5\\approx":[244],"1.857+\u03b5$.":[245],"Finally,":[246],"establish":[248],"lower":[250],"bound":[251],"$n^{\u03a9(1/\u03b5)}$":[253],"running":[256],"$(1+\u03b5)$-approximation":[260],"our":[263],"or":[266],"--":[269],"setting,":[274],"assuming":[275],"$k$-\\textsc{Sum}":[277],"Conjecture.":[278]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-27T00:00:00"}
