{"id":"https://openalex.org/W39861960","doi":"https://doi.org/10.4086/toc.2010.v006a011","title":"","display_name":"","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W39861960","doi":"https://doi.org/10.4086/toc.2010.v006a011","mag":"39861960"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2010.v006a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a011","pdf_url":"https://theoryofcomputing.org/articles/v006a011/v006a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"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","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v006a011/v006a011.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013190102","display_name":"Uriel Feige","orcid":"https://orcid.org/0009-0006-3749-4392"},"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"]},{"id":"https://openalex.org/I4210155201","display_name":"Redmond Fire Department","ror":"https://ror.org/05d788x61","country_code":"US","type":"government","lineage":["https://openalex.org/I4210155201"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Uriel Feige","raw_affiliation_strings":["Redmond, WA","Microsoft Research, Redmond, WA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Redmond, WA","institution_ids":["https://openalex.org/I4210155201"]},{"raw_affiliation_string":"Microsoft Research, Redmond, WA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023410548","display_name":"Jan Vondr\u00e1k","orcid":"https://orcid.org/0000-0001-7568-6711"},"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"]},{"id":"https://openalex.org/I4210155201","display_name":"Redmond Fire Department","ror":"https://ror.org/05d788x61","country_code":"US","type":"government","lineage":["https://openalex.org/I4210155201"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jan Vondrak","raw_affiliation_strings":["Redmond, WA","Microsoft Research, Redmond, WA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Redmond, WA","institution_ids":["https://openalex.org/I4210155201"]},{"raw_affiliation_string":"Microsoft Research, Redmond, WA","institution_ids":["https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3828,"has_fulltext":true,"cited_by_count":81,"citation_normalized_percentile":{"value":0.91764661,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"6","issue":"1","first_page":"247","last_page":"290"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9991000294685364,"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/T10237","display_name":"Cryptography and Data Security","score":0.9962999820709229,"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/submodular-set-function","display_name":"Submodular set function","score":0.9377590417861938},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.6847212314605713},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6334739923477173},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6274555325508118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.620421290397644},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5920577049255371},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5586040019989014},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4690459370613098},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.46688809990882874},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4395330846309662},{"id":"https://openalex.org/keywords/incentive-compatibility","display_name":"Incentive compatibility","score":0.4350929260253906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19180458784103394},{"id":"https://openalex.org/keywords/incentive","display_name":"Incentive","score":0.12238600850105286}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.9377590417861938},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.6847212314605713},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6334739923477173},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6274555325508118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.620421290397644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5920577049255371},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5586040019989014},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4690459370613098},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.46688809990882874},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4395330846309662},{"id":"https://openalex.org/C91810955","wikidata":"https://www.wikidata.org/wiki/Q7731670","display_name":"Incentive compatibility","level":3,"score":0.4350929260253906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19180458784103394},{"id":"https://openalex.org/C29122968","wikidata":"https://www.wikidata.org/wiki/Q1414816","display_name":"Incentive","level":2,"score":0.12238600850105286},{"id":"https://openalex.org/C175444787","wikidata":"https://www.wikidata.org/wiki/Q39072","display_name":"Microeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2010.v006a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a011","pdf_url":"https://theoryofcomputing.org/articles/v006a011/v006a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"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","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2010.v006a011","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2010.v006a011","pdf_url":"https://theoryofcomputing.org/articles/v006a011/v006a011.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"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","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W39861960.pdf","grobid_xml":"https://content.openalex.org/works/W39861960.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1511472641","https://openalex.org/W1515157528","https://openalex.org/W1579522749","https://openalex.org/W1607066202","https://openalex.org/W1680189815","https://openalex.org/W1989453388","https://openalex.org/W2013469527","https://openalex.org/W2022749618","https://openalex.org/W2035337032","https://openalex.org/W2059453880","https://openalex.org/W2081254453","https://openalex.org/W2104334470","https://openalex.org/W2115435070","https://openalex.org/W2126085282","https://openalex.org/W2126307323","https://openalex.org/W2129866531","https://openalex.org/W2143996311","https://openalex.org/W2161272173","https://openalex.org/W2621717961","https://openalex.org/W2757107770","https://openalex.org/W2962711478","https://openalex.org/W3008429003","https://openalex.org/W3118655244","https://openalex.org/W4238439820","https://openalex.org/W4245400518"],"related_works":["https://openalex.org/W1595919516","https://openalex.org/W2945022594","https://openalex.org/W2966531942","https://openalex.org/W2194604332","https://openalex.org/W1608444752","https://openalex.org/W2950365512","https://openalex.org/W3204684126","https://openalex.org/W2062310236","https://openalex.org/W3013568067","https://openalex.org/W4299354108"],"abstract_inverted_index":{"We":[0,36,84],"consider":[1],"the":[2,73],"Submodular":[3],"Welfare":[4],"Problem":[5],"where":[6],"we":[7],"have":[8],"m":[9],"items":[10,58],"and":[11,34,82],"n":[12,56],"players":[13],"with":[14],"given":[15,79],"utility":[16,27],"functions":[17,28],"w":[18,61],"i":[19,60,62,64],":":[20],"2":[21,49],"[m]":[22],"R":[23],"+":[24,93],".":[25,51,52,53],"The":[26],"are":[29],"assumed":[30],"to":[31,38],"be":[32],"monotone":[33],"submodular.":[35],"want":[37],"find":[39],"an":[40],"allocation":[41],"of":[42,57],"disjoint":[43],"sets":[44],"S":[45,48,55],"1":[46],",":[47,50,54],"maximizing":[59],"(S":[63],").":[65],"A":[66],"(1":[67,91],"-1/e)-approximation":[68],"for":[69,95],"this":[70,86],"problem":[71],"in":[72],"demand":[74],"oracle":[75],"model":[76],"has":[77],"been":[78],"by":[80,88],"Dobzinski":[81],"Schapira":[83],"improve":[85],"algorithm":[87],"presenting":[89],"a":[90],"-1/e":[92],")-approximation":[94],"some":[96],"small":[97],"fixed":[98],">":[99],"0.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":1}],"updated_date":"2025-12-17T22:08:43.090829","created_date":"2016-06-24T00:00:00"}
