{"id":"https://openalex.org/W2041375228","doi":"https://doi.org/10.1145/2746539.2746589","title":"Approximating the Nash Social Welfare with Indivisible Items","display_name":"Approximating the Nash Social Welfare with Indivisible Items","publication_year":2015,"publication_date":"2015-06-03","ids":{"openalex":"https://openalex.org/W2041375228","doi":"https://doi.org/10.1145/2746539.2746589","mag":"2041375228"},"language":"en","primary_location":{"id":"doi:10.1145/2746539.2746589","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2746539.2746589","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5042866153","display_name":"Richard Cole","orcid":"https://orcid.org/0000-0002-5885-0222"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Cole","raw_affiliation_strings":["New York University, New York, NY, USA","New York University,New York,NY,USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New York University, New York, NY, USA","institution_ids":["https://openalex.org/I57206974"]},{"raw_affiliation_string":"New York University,New York,NY,USA","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055235820","display_name":"Vasilis Gkatzelis","orcid":"https://orcid.org/0000-0001-7203-438X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vasilis Gkatzelis","raw_affiliation_strings":["Stanford University, Stanford, CA, USA","Stanford Univ., Stanford, CA (USA)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Stanford Univ., Stanford, CA (USA)","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":83,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"371","last_page":"380"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.6053183674812317},{"id":"https://openalex.org/keywords/welfare","display_name":"Welfare","score":0.575579822063446},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5491745471954346},{"id":"https://openalex.org/keywords/social-welfare","display_name":"Social Welfare","score":0.5383850336074829},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.346259742975235},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.28175419569015503},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.12240082025527954}],"concepts":[{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.6053183674812317},{"id":"https://openalex.org/C100243477","wikidata":"https://www.wikidata.org/wiki/Q12002092","display_name":"Welfare","level":2,"score":0.575579822063446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5491745471954346},{"id":"https://openalex.org/C536738050","wikidata":"https://www.wikidata.org/wiki/Q3249071","display_name":"Social Welfare","level":2,"score":0.5383850336074829},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.346259742975235},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.28175419569015503},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.12240082025527954},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2746539.2746589","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2746539.2746589","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.712.2470","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.712.2470","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.stanford.edu/%7Egkatz/NashSW.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7721793150","display_name":null,"funder_award_id":"CCF-1215965, CCF-1217989","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W64178506","https://openalex.org/W1482334512","https://openalex.org/W1577069963","https://openalex.org/W1857915517","https://openalex.org/W1978593916","https://openalex.org/W1980938853","https://openalex.org/W1987497363","https://openalex.org/W2001927417","https://openalex.org/W2005723304","https://openalex.org/W2008751404","https://openalex.org/W2017990047","https://openalex.org/W2023581071","https://openalex.org/W2027473833","https://openalex.org/W2049051180","https://openalex.org/W2050020465","https://openalex.org/W2053060972","https://openalex.org/W2079854492","https://openalex.org/W2080780366","https://openalex.org/W2095794917","https://openalex.org/W2114725112","https://openalex.org/W2118008360","https://openalex.org/W2121240598","https://openalex.org/W2150409561","https://openalex.org/W2159715570","https://openalex.org/W2508573783","https://openalex.org/W2736305340","https://openalex.org/W2776361207","https://openalex.org/W4236082126","https://openalex.org/W4247772422","https://openalex.org/W6635888730","https://openalex.org/W6648571123","https://openalex.org/W6661178039","https://openalex.org/W6818369698"],"related_works":["https://openalex.org/W1554758635","https://openalex.org/W2500870930","https://openalex.org/W2569414037","https://openalex.org/W2218535193","https://openalex.org/W2791846392","https://openalex.org/W2978736442","https://openalex.org/W2293139794","https://openalex.org/W2000605526","https://openalex.org/W3175476170","https://openalex.org/W3201903812"],"abstract_inverted_index":{"We":[0,54],"study":[1],"the":[2,17,21,25,29,45,58,62],"problem":[3,34],"of":[4,8,19,24,61],"allocating":[5],"a":[6,71,77,86],"set":[7],"indivisible":[9],"items":[10],"among":[11],"agents":[12],"with":[13,16],"additive":[14],"valuations,":[15,27],"goal":[18],"maximizing":[20],"geometric":[22],"mean":[23],"agents'":[26],"i.e.,":[28],"Nash":[30],"social":[31],"welfare.":[32],"This":[33],"is":[35,44,66],"known":[36],"to":[37],"be":[38],"NP-hard,":[39],"and":[40],"our":[41],"main":[42],"result":[43],"first":[46,55],"efficient":[47],"constant-factor":[48],"approximation":[49],"algorithm":[50],"for":[51],"this":[52],"objective.":[53],"observe":[56],"that":[57],"integrality":[59],"gap":[60],"natural":[63],"fractional":[64,73],"relaxation":[65],"exponential,":[67],"so":[68],"we":[69],"propose":[70],"different":[72],"allocation":[74],"which":[75],"implies":[76],"tighter":[78],"upper":[79],"bound":[80],"and,":[81],"after":[82],"appropriate":[83],"rounding,":[84],"yields":[85],"good":[87],"integral":[88],"allocation.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
