{"id":"https://openalex.org/W2962836029","doi":"https://doi.org/10.4230/lipics.itcs.2017.36","title":"Nash Social Welfare, Matrix Permanent, and Stable Polynomials","display_name":"Nash Social Welfare, Matrix Permanent, and Stable Polynomials","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2962836029","doi":"https://doi.org/10.4230/lipics.itcs.2017.36","mag":"2962836029"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:8148","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.36","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.36","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040375566","display_name":"Nima Anari","orcid":"https://orcid.org/0000-0002-4394-3530"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Anari, Nima","raw_affiliation_strings":["University of California, Berkeley, Berkeley, United States"],"affiliations":[{"raw_affiliation_string":"University of California, Berkeley, Berkeley, United States","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017101724","display_name":"Shayan Oveis Gharan","orcid":"https://orcid.org/0000-0002-5504-0849"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I58610484","display_name":"Seattle University","ror":"https://ror.org/02jqc0m91","country_code":"US","type":"education","lineage":["https://openalex.org/I58610484"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Oveis Gharan, Shayan","raw_affiliation_strings":["University of Washington, Seattle, United States"],"affiliations":[{"raw_affiliation_string":"University of Washington, Seattle, United States","institution_ids":["https://openalex.org/I58610484","https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001035442","display_name":"Amin Saberi","orcid":"https://orcid.org/0000-0002-7043-0722"},"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":"Saberi, Amin","raw_affiliation_strings":["Stanford University, Stanford, United States"],"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, United States","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020914506","display_name":"Mohit Singh","orcid":"https://orcid.org/0000-0002-0827-233X"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Singh, Mohit","raw_affiliation_strings":["Microsoft (United States), Redmond, United States"],"affiliations":[{"raw_affiliation_string":"Microsoft (United States), Redmond, United States","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040375566"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":21.1416,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.98983074,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"67","issue":null,"first_page":"12","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9948999881744385,"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":0.9948999881744385,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9947999715805054,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9904999732971191,"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/monomial","display_name":"Monomial","score":0.6065878868103027},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5992728471755981},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5273289084434509},{"id":"https://openalex.org/keywords/randomized-rounding","display_name":"Randomized rounding","score":0.5271382331848145},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5242262482643127},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.49599751830101013},{"id":"https://openalex.org/keywords/nash-equilibrium","display_name":"Nash equilibrium","score":0.48033514618873596},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43217360973358154},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.4105808734893799},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40767812728881836},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4038843810558319},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3880666494369507},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.3300807476043701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2201477289199829}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.6065878868103027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5992728471755981},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5273289084434509},{"id":"https://openalex.org/C32029473","wikidata":"https://www.wikidata.org/wiki/Q7292010","display_name":"Randomized rounding","level":3,"score":0.5271382331848145},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5242262482643127},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.49599751830101013},{"id":"https://openalex.org/C46814582","wikidata":"https://www.wikidata.org/wiki/Q23389","display_name":"Nash equilibrium","level":2,"score":0.48033514618873596},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43217360973358154},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.4105808734893799},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40767812728881836},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4038843810558319},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3880666494369507},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3300807476043701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2201477289199829},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:8148","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.36","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},{"id":"doi:10.4230/lipics.itcs.2017.36","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.itcs.2017.36","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":""},{"id":"mag:2962836029","is_oa":false,"landing_page_url":"https://drops.dagstuhl.de/opus/volltexte/2017/8148/pdf/LIPIcs-ITCS-2017-36.pdf/","pdf_url":null,"source":{"id":"https://openalex.org/S4306418069","display_name":"Conference on Innovations in Theoretical Computer Science","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Conference on Innovations in Theoretical Computer Science","raw_type":null}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:8148","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.36","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G4274955751","display_name":"AF: Small: Rounding by Sampling Method and Applications to Traveling Salesman Problems","funder_award_id":"1216698","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2584164274","https://openalex.org/W2346164124","https://openalex.org/W2522115756","https://openalex.org/W2963034101","https://openalex.org/W2962812754","https://openalex.org/W2041375228","https://openalex.org/W2963444396","https://openalex.org/W2963475394","https://openalex.org/W1577069963","https://openalex.org/W2150409561","https://openalex.org/W2121240598","https://openalex.org/W2527398973","https://openalex.org/W3001493365","https://openalex.org/W3144138375","https://openalex.org/W2017990047","https://openalex.org/W2017970485","https://openalex.org/W1980938853","https://openalex.org/W2592030152","https://openalex.org/W2119085547","https://openalex.org/W2022749618"],"abstract_inverted_index":{"We":[0,20,87],"study":[1],"the":[2,14,45,48,68,71,93,97],"problem":[3],"of":[4,44,52,63,70,74,96],"allocating":[5],"m":[6,81],"items":[7],"to":[8,12,83,91],"n":[9],"agents":[10],"subject":[11],"maximizing":[13],"Nash":[15],"social":[16],"welfare":[17,95],"(NSW)":[18],"objective.":[19],"write":[21],"a":[22,34,40,75],"novel":[23],"convex":[24],"programming":[25],"relaxation":[26],"for":[27],"this":[28,89],"problem,":[29],"and":[30,54],"we":[31],"show":[32],"that":[33],"simple":[35],"randomized":[36,102],"rounding":[37,103],"algorithm":[38],"gives":[39],"1/e":[41],"approximation":[42,50],"factor":[43,51],"objective,":[46],"breaking":[47],"1/2e^(1/e)":[49],"Cole":[53],"Gkatzelis.":[55],"Our":[56],"main":[57],"technical":[58],"contribution":[59],"is":[60],"an":[61],"extension":[62,90],"Gurvits's":[64],"lower":[65],"bound":[66],"on":[67,80],"coefficient":[69],"square-free":[72],"monomial":[73],"degree":[76],"m-homogeneous":[77],"stable":[78],"polynomial":[79],"variables":[82],"all":[84],"homogeneous":[85],"polynomials.":[86],"use":[88],"analyze":[92],"expected":[94],"allocation":[98],"returned":[99],"by":[100],"our":[101],"algorithm.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
