{"id":"https://openalex.org/W4408031903","doi":"https://doi.org/10.1007/s00224-025-10215-0","title":"Online Unbounded Knapsack","display_name":"Online Unbounded Knapsack","publication_year":2025,"publication_date":"2025-03-01","ids":{"openalex":"https://openalex.org/W4408031903","doi":"https://doi.org/10.1007/s00224-025-10215-0"},"language":"en","primary_location":{"id":"doi:10.1007/s00224-025-10215-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-025-10215-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-025-10215-0.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","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/s00224-025-10215-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086921684","display_name":"Hans-Joachim B\u00f6ckenhauer","orcid":"https://orcid.org/0000-0001-9164-3674"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Hans-Joachim B\u00f6ckenhauer","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057719906","display_name":"Matthias Gehnen","orcid":"https://orcid.org/0000-0001-9595-2992"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Gehnen","raw_affiliation_strings":["Department of Computer Science, RWTH Aachen, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, RWTH Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088678782","display_name":"Juraj Hromkovi\u010d","orcid":"https://orcid.org/0000-0001-9754-7042"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Juraj Hromkovi\u010d","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112786437","display_name":"Ralf Klasing","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ralf Klasing","raw_affiliation_strings":["CNRS, LaBRI, Universit\u00e9 de Bordeaux, Talence, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS, LaBRI, Universit\u00e9 de Bordeaux, Talence, France","institution_ids":["https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210160189","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033151596","display_name":"Dennis Komm","orcid":"https://orcid.org/0000-0002-9024-1558"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Dennis Komm","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079384609","display_name":"Henri Lotze","orcid":"https://orcid.org/0000-0001-5013-8831"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Henri Lotze","raw_affiliation_strings":["Department of Computer Science, RWTH Aachen, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, RWTH Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053133051","display_name":"Daniel Mock","orcid":"https://orcid.org/0000-0002-0011-6754"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Daniel Mock","raw_affiliation_strings":["Department of Computer Science, RWTH Aachen, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, RWTH Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062653045","display_name":"Peter Rossmanith","orcid":"https://orcid.org/0000-0003-0177-8028"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Rossmanith","raw_affiliation_strings":["Department of Computer Science, RWTH Aachen, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, RWTH Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103042020","display_name":"Moritz Stocker","orcid":"https://orcid.org/0009-0003-8754-5301"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Moritz Stocker","raw_affiliation_strings":["Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, ETH Z\u00fcrich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":9,"corresponding_author_ids":["https://openalex.org/A5086921684"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.2851,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78352909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"69","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9998000264167786,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9890999794006348,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11567","display_name":"semigroups and automata theory","score":0.9890000224113464,"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":0.841875433921814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4476920962333679},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4208592176437378},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.18060237169265747}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.841875433921814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4476920962333679},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4208592176437378},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.18060237169265747}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00224-025-10215-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-025-10215-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-025-10215-0.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05352178v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05352178","pdf_url":"https://hal.science/hal-05352178/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"Theory of Computing Systems, 2025, 69 (1), pp.14. &#x27E8;10.1007/s00224-025-10215-0&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s00224-025-10215-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00224-025-10215-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00224-025-10215-0.pdf","source":{"id":"https://openalex.org/S4210177266","display_name":"Theory of Computing Systems","issn_l":"1432-4350","issn":["1432-4350","1433-0490"],"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":"Theory of Computing Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2465436510","display_name":null,"funder_award_id":"ANR-22-CE48-0001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4715010108","display_name":null,"funder_award_id":"22-CE48-0001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408031903.pdf"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W1512794094","https://openalex.org/W1542204506","https://openalex.org/W1552828154","https://openalex.org/W1554718677","https://openalex.org/W1589175915","https://openalex.org/W1884349932","https://openalex.org/W1970970009","https://openalex.org/W2011039300","https://openalex.org/W2025034398","https://openalex.org/W2026891055","https://openalex.org/W2038319432","https://openalex.org/W2041645394","https://openalex.org/W2055756370","https://openalex.org/W2060023372","https://openalex.org/W2066898525","https://openalex.org/W2067500652","https://openalex.org/W2081136687","https://openalex.org/W2090987741","https://openalex.org/W2099519545","https://openalex.org/W2109659895","https://openalex.org/W2112906671","https://openalex.org/W2113195911","https://openalex.org/W2131397354","https://openalex.org/W2142199526","https://openalex.org/W2401610261","https://openalex.org/W2595319805","https://openalex.org/W2606892140","https://openalex.org/W2626350546","https://openalex.org/W2751193914","https://openalex.org/W2807933378","https://openalex.org/W2809834751","https://openalex.org/W2885283474","https://openalex.org/W2887005261","https://openalex.org/W2893780080","https://openalex.org/W2900579929","https://openalex.org/W2936175778","https://openalex.org/W2942755285","https://openalex.org/W2977477903","https://openalex.org/W3001957700","https://openalex.org/W3003610019","https://openalex.org/W3031442975","https://openalex.org/W3112854149","https://openalex.org/W3122069597","https://openalex.org/W3138989795","https://openalex.org/W3158056478","https://openalex.org/W3174405270","https://openalex.org/W3174973330","https://openalex.org/W4220702923","https://openalex.org/W4236127247","https://openalex.org/W4240438018","https://openalex.org/W4287781747","https://openalex.org/W4292845823","https://openalex.org/W4294631421","https://openalex.org/W4300027202","https://openalex.org/W4320022257","https://openalex.org/W4320830016","https://openalex.org/W4379118066","https://openalex.org/W4379134737","https://openalex.org/W4387336218","https://openalex.org/W4392381171","https://openalex.org/W6833034547","https://openalex.org/W6891368410"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W241127407","https://openalex.org/W2381035939","https://openalex.org/W2468477307","https://openalex.org/W2910645127","https://openalex.org/W162895179","https://openalex.org/W1521824362","https://openalex.org/W2168163332"],"abstract_inverted_index":{"Abstract":[0],"We":[1,117,143,372,400,456],"analyze":[2,145],"the":[3,7,11,61,65,71,75,80,84,96,102,106,120,126,154,170,191,205,217,226,403],"competitive":[4,139,171,227,277,419,521],"ratio":[5,140,172,228,278,420,522],"and":[6,29,33,42,60,148,409,424],"advice":[8,192,203,223,268,351,379,454,516],"complexity":[9,193],"of":[10,23,52,64,83,128,141,200,272,279,378,523],"online":[12,59,404],"unbounded":[13,107,122,219,406],"knapsack":[14,51,98,104,123,156,220,407],"problem.":[15],"An":[16],"instance":[17],"is":[18,77,131],"given":[19,58],"as":[20,427,429],"a":[21,27,30,50,138,276,382,459,520],"sequence":[22],"n":[24,274],"items":[25,56,67,111],"with":[26,245,299],"size":[28,63,127],"value":[31,82],"each,":[32],"an":[34,164,395],"algorithm":[35,206,396,462],"has":[36,207],"to":[37,45,78,112,133,153,173,208,210,229,397,518],"decide":[38],"whether":[39],"or":[40],"not":[41,69,414],"how":[43,197],"often":[44],"pack":[46],"each":[47,88,129],"item":[48,89,130],"into":[49],"bounded":[53,380,418],"capacity.":[54],"The":[55],"are":[57],"total":[62,81],"packed":[66,85,93,114],"must":[68],"exceed":[70],"knapsack\u2019s":[72],"capacity,":[73],"while":[74],"objective":[76],"maximize":[79],"items.":[86],"While":[87,240],"can":[90,182,296],"only":[91],"be":[92,113,184,243,297,398],"once":[94],"in":[95,151],"classical":[97],"problem":[99,408],"(also":[100],"called":[101],"0-1":[103,155],"problem),":[105],"version":[108],"allows":[109,136,394],"for":[110,137,270,353,416,421,430],"multiple":[115],"times.":[116],"show":[118,149,374,410],"that":[119,375,411,463],"simple":[121,218,461],"problem,":[124,157,221],"where":[125],"equal":[132],"its":[134],"value,":[135],"2.":[142],"also":[144,401,457],"randomized":[146,425],"algorithms":[147,431],"that,":[150],"contrast":[152],"one":[158,222],"uniformly":[159],"random":[160],"bit":[161,224],"cannot":[162,242],"improve":[163],"algorithm\u2019s":[165],"performance.":[166],"More":[167],"randomness":[168],"lowers":[169,225],"less":[174],"than":[175,247,434],"1":[176,186],".":[177,187,189,239,371],"736":[178],",":[179,275],"but":[180],"it":[181,412],"never":[183],"below":[185],"693":[188],"In":[190],"setting,":[194],"we":[195],"measure":[196],"many":[198],"bits":[199,269,352,517],"information":[201],"(so-called":[202],"bits)":[204],"know":[209],"achieve":[211,519],"some":[212],"desired":[213],"solution":[214],"quality.":[215],"For":[216],"$$\\varvec{3/2}$$":[230],"<mml:math":[231,252,282,306,357,385,438,471],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[232,253,283,307,358,386,439,472],"<mml:mrow>":[233,254,256,259,263,284,285,288,291,308,309,312,316,319,324,327,330,333,337,340,345,359,360,363,366,387,440,442,445,449,473,474,477,481,484,489,492,495,498,502,505,510],"<mml:mn>3</mml:mn>":[234],"<mml:mo>/</mml:mo>":[235],"<mml:mn>2</mml:mn>":[236,260,446],"</mml:mrow>":[237,258,261,265,266,287,290,293,294,311,314,318,322,326,329,332,335,339,343,348,349,362,365,368,369,392,444,447,451,452,476,479,483,487,491,494,497,500,504,508,513,514],"</mml:math>":[238,267,295,350,370,393,453,515],"this":[241],"improved":[244],"fewer":[246,433],"$$\\varvec{\\log":[248,435],"}_{\\varvec{2}}":[249,436],"\\varvec{n}":[250],"$$":[251],"<mml:msub>":[255,441],"<mml:mo>log</mml:mo>":[257,328,443,493],"</mml:msub>":[262,448],"<mml:mi>n</mml:mi>":[264,334,390,450,499],"instances":[271],"length":[273],"$$\\varvec{1}\\varvec{+}\\varvec{\\varepsilon":[280],"}$$":[281],"<mml:mn>1</mml:mn>":[286,321,342,486,507],"<mml:mo>+</mml:mo>":[289],"<mml:mi>\u03b5</mml:mi>":[292,317,338,361,482,503],"achieved":[298],"$$\\varvec{O}\\varvec{(}\\varvec{\\varepsilon":[300,465],"}^{\\varvec{-1}}":[301,466],"\\varvec{\\cdot":[302,467],"}\\varvec{\\log":[303,468],"}\\varvec{(}\\varvec{n}\\varvec{\\varepsilon":[304,469],"}^{\\varvec{-1}}\\varvec{))}$$":[305,470],"<mml:mi>O</mml:mi>":[310,475],"<mml:mo>(</mml:mo>":[313,331,389,478,496],"<mml:msup>":[315,336,480,501],"<mml:mo>-</mml:mo>":[320,341,485,506],"</mml:msup>":[323,344,488,509],"<mml:mo>\u00b7</mml:mo>":[325,490],"<mml:mo>)</mml:mo>":[346,347,391,511,512],"any":[354,417],"$$\\varvec{\\varepsilon":[355],"}\\varvec{&gt;}\\varvec{0}$$":[356],"<mml:mo>&gt;</mml:mo>":[364],"<mml:mn>0</mml:mn>":[367],"further":[373],"no":[376],"amount":[377],"by":[381],"function":[383],"$$\\varvec{f(n)}$$":[384],"<mml:mi>f</mml:mi>":[388],"optimal.":[399],"study":[402],"general":[405],"does":[413],"allow":[415],"both":[422],"deterministic":[423],"algorithms,":[426],"well":[428],"using":[432],"\\varvec{n}$$":[437],"bits.":[455],"provide":[458],"surprisingly":[460],"uses":[464],"<jats:tex":[524]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
