{"id":"https://openalex.org/W3143775817","doi":"https://doi.org/10.1287/moor.2020.1088","title":"Tight Approximation for Unconstrained XOS Maximization","display_name":"Tight Approximation for Unconstrained XOS Maximization","publication_year":2021,"publication_date":"2021-03-29","ids":{"openalex":"https://openalex.org/W3143775817","doi":"https://doi.org/10.1287/moor.2020.1088","mag":"3143775817"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2020.1088","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2020.1088","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations 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/A5047362769","display_name":"Yuval Filmus","orcid":"https://orcid.org/0000-0002-1739-0872"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Yuval Filmus","raw_affiliation_strings":["The Henry and Marilyn Taub Faculty of Computer Science, Technion\u2013Israel Institute of Technology, Haifa 3200003, Israel;"],"affiliations":[{"raw_affiliation_string":"The Henry and Marilyn Taub Faculty of Computer Science, Technion\u2013Israel Institute of Technology, Haifa 3200003, Israel;","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025634820","display_name":"Yasushi Kawase","orcid":"https://orcid.org/0000-0001-5626-779X"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasushi Kawase","raw_affiliation_strings":["Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan;"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan;","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074548000","display_name":"Yusuke Kobayashi","orcid":"https://orcid.org/0000-0001-9478-7307"},"institutions":[{"id":"https://openalex.org/I22299242","display_name":"Kyoto University","ror":"https://ror.org/02kpeqv85","country_code":"JP","type":"education","lineage":["https://openalex.org/I22299242"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yusuke Kobayashi","raw_affiliation_strings":["Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan;"],"affiliations":[{"raw_affiliation_string":"Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan;","institution_ids":["https://openalex.org/I22299242"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039274625","display_name":"Yutaro Yamaguchi","orcid":"https://orcid.org/0000-0002-1919-7195"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yutaro Yamaguchi","raw_affiliation_strings":["Graduate School and Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka 819-0395, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School and Faculty of Information Science and Electrical Engineering, Kyushu University, Fukuoka 819-0395, Japan","institution_ids":["https://openalex.org/I135598925"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5047362769"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06932886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"4","first_page":"1599","last_page":"1610"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T12288","display_name":"Optimization and Search Problems","score":0.9994999766349792,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8825831413269043},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.617861270904541},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.609890878200531},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5345375537872314},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5244020223617554},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.49913454055786133},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.49834585189819336},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4913147985935211},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.46204066276550293},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43706241250038147},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.43473923206329346},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.42788833379745483},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17296600341796875},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.115335613489151}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8825831413269043},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.617861270904541},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.609890878200531},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5345375537872314},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5244020223617554},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.49913454055786133},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.49834585189819336},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4913147985935211},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.46204066276550293},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43706241250038147},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.43473923206329346},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.42788833379745483},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17296600341796875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.115335613489151},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1287/moor.2020.1088","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2020.1088","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:inm:ormoor:v:46:y:2021:i:4:p:1599-1610","is_oa":false,"landing_page_url":"http://doi.org/10.1287/moor.2020.1088","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":23,"referenced_works":["https://openalex.org/W1680189815","https://openalex.org/W1875347116","https://openalex.org/W1975378045","https://openalex.org/W1991223607","https://openalex.org/W1997783781","https://openalex.org/W2012329067","https://openalex.org/W2033885045","https://openalex.org/W2035575256","https://openalex.org/W2053381548","https://openalex.org/W2057929994","https://openalex.org/W2059527251","https://openalex.org/W2100440346","https://openalex.org/W2105296258","https://openalex.org/W2109309418","https://openalex.org/W2128059732","https://openalex.org/W2132651631","https://openalex.org/W2133040106","https://openalex.org/W2179494254","https://openalex.org/W2883525063","https://openalex.org/W2962711478","https://openalex.org/W3160905013","https://openalex.org/W4231868828","https://openalex.org/W4255179538"],"related_works":["https://openalex.org/W2073713056","https://openalex.org/W3110702597","https://openalex.org/W2125620709","https://openalex.org/W2110441383","https://openalex.org/W2045932760","https://openalex.org/W4233149903","https://openalex.org/W2326878701","https://openalex.org/W4293864700","https://openalex.org/W2184228419","https://openalex.org/W67445448"],"abstract_inverted_index":{"A":[0],"set":[1,124],"function":[2,33,178],"is":[3,21,34,56,72,79,103,117,121,135,146,201],"called":[4,35],"XOS":[5,32,47,60,133,177],"if":[6,115],"it":[7,71],"can":[8],"be":[9],"represented":[10],"by":[11,137],"the":[12,23,31,36,43,50,59,77,91,100,122,128,131,143,199],"maximum":[13],"of":[14,25,45,62,87,130,174,179,193],"additive":[15,26],"functions.":[16],"When":[17],"such":[18],"a":[19,138,166,175],"representation":[20],"fixed,":[22],"number":[24,192],"functions":[27,48,61,134],"required":[28],"to":[29,81,169,203],"define":[30],"width.":[37],"In":[38,162],"this":[39,95],"paper,":[40],"we":[41,164,183],"study":[42],"problem":[44,55],"maximizing":[46],"in":[49,98],"value":[51,194],"oracle":[52,195],"model.":[53],"The":[54],"trivial":[57],"for":[58,94,157],"width":[63,78,129,180,200],"1":[64,150,154],"because":[65],"they":[66],"are":[67],"just":[68],"additive,":[69],"but":[70],"already":[73],"nontrivial":[74],"even":[75,197],"when":[76,127,198],"restricted":[80,202],"2.":[82],"We":[83],"show":[84,184],"two":[85],"types":[86],"tight":[88],"bounds":[89],"on":[90],"polynomial-time":[92],"approximability":[93],"problem.":[96],"First,":[97],"general,":[99],"approximation":[101,144],"bound":[102,145],"between":[104,147],"O(n)":[105],"and":[106,110,151],"[Formula:":[107,112],"see":[108,113],"text],":[109],"exactly":[111],"text]":[114],"randomization":[116],"allowed,":[118],"where":[119],"n":[120],"ground":[123],"size.":[125],"Second,":[126],"input":[132],"bounded":[136],"constant":[139],"k":[140,148,152],"\u2265":[141],"2,":[142,181],"\u2212":[149,153,155],"\u025b":[156,159],"any":[158,186],">":[160],"0.":[161],"particular,":[163],"give":[165],"linear-time":[167],"algorithm":[168,188],"find":[170],"an":[171,190],"exact":[172,187],"maximizer":[173],"given":[176],"whereas":[182],"that":[185],"requires":[189],"exponential":[191],"calls":[196],"3.":[204]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}