{"id":"https://openalex.org/W4226529202","doi":"https://doi.org/10.48550/arxiv.2204.10322","title":"Online Two-Dimensional Vector Packing with Advice","display_name":"Online Two-Dimensional Vector Packing with Advice","publication_year":2022,"publication_date":"2022-04-21","ids":{"openalex":"https://openalex.org/W4226529202","doi":"https://doi.org/10.48550/arxiv.2204.10322"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2204.10322","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.10322","pdf_url":"https://arxiv.org/pdf/2204.10322","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2204.10322","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101713320","display_name":"Bengt J. Nilsson","orcid":"https://orcid.org/0000-0002-1342-8618"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nilsson, Bengt J.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078463139","display_name":"Gordana Vujovi\u0107","orcid":"https://orcid.org/0000-0001-5283-3440"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vujovic, Gordana","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101713320"],"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/T12288","display_name":"Optimization and Search Problems","score":0.9993000030517578,"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":0.9993000030517578,"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/T12176","display_name":"Optimization and Packing Problems","score":0.9864000082015991,"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/T11182","display_name":"Auction Theory and Applications","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/advice","display_name":"Advice (programming)","score":0.8004204034805298},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.7832260131835938},{"id":"https://openalex.org/keywords/competitive-analysis","display_name":"Competitive analysis","score":0.6365757584571838},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5743021965026855},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5580835938453674},{"id":"https://openalex.org/keywords/pi","display_name":"Pi","score":0.5354153513908386},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.44833239912986755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41267552971839905},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.39459002017974854},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.21708926558494568},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19795364141464233},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19479870796203613},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18335944414138794},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0849444568157196}],"concepts":[{"id":"https://openalex.org/C2779955035","wikidata":"https://www.wikidata.org/wiki/Q4686785","display_name":"Advice (programming)","level":2,"score":0.8004204034805298},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7832260131835938},{"id":"https://openalex.org/C102408133","wikidata":"https://www.wikidata.org/wiki/Q5156350","display_name":"Competitive analysis","level":3,"score":0.6365757584571838},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5743021965026855},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5580835938453674},{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.5354153513908386},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.44833239912986755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41267552971839905},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39459002017974854},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.21708926558494568},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19795364141464233},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19479870796203613},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18335944414138794},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0849444568157196},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2204.10322","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.10322","pdf_url":"https://arxiv.org/pdf/2204.10322","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2204.10322","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2204.10322","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2204.10322","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2204.10322","pdf_url":"https://arxiv.org/pdf/2204.10322","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4393601209","https://openalex.org/W2030762054","https://openalex.org/W3157618815","https://openalex.org/W2401345448","https://openalex.org/W2797367353","https://openalex.org/W2223743052","https://openalex.org/W2746357114","https://openalex.org/W2481908560","https://openalex.org/W2521648624","https://openalex.org/W2620689363"],"abstract_inverted_index":{"We":[0,26],"consider":[1],"the":[2,15,24,41,50],"online":[3],"two-dimensional":[4],"vector":[5],"packing":[6],"problem,":[7],"showing":[8],"a":[9],"lower":[10],"bound":[11],"of":[12,18],"$11/5$":[13],"on":[14],"competitive":[16,30],"ratio":[17,31],"any":[19,37],"{\\sc":[20],"AnyFit}":[21],"strategy":[22],"for":[23,36,53],"problem.":[25],"provide":[27],"strategies":[28],"with":[29],"$\\max\\!\\left\\{2,6\\big/\\big(1+3\\tan(\u03c0/4-\u03b3/2)\\big)+\u03b5\\right\\}$":[32],"and":[33],"logarithmic":[34],"advice,":[35],"instance":[38],"where":[39],"all":[40],"input":[42],"vectors":[43],"are":[44],"restricted":[45],"to":[46],"have":[47],"angles":[48],"in":[49],"range":[51],"$[\u03c0/4-\u03b3/2,\u03c0/4+\u03b3/2]$,":[52],"$0\\leq\u03b3":[54]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}
