{"id":"https://openalex.org/W2053381548","doi":"https://doi.org/10.1137/090779346","title":"Maximizing Non-monotone Submodular Functions","display_name":"Maximizing Non-monotone Submodular Functions","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2053381548","doi":"https://doi.org/10.1137/090779346","mag":"2053381548"},"language":"en","primary_location":{"id":"doi:10.1137/090779346","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090779346","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5013190102","display_name":"Uriel Feige","orcid":"https://orcid.org/0009-0006-3749-4392"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Uriel Feige","raw_affiliation_strings":["uriel.feige@weizmann.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"uriel.feige@weizmann.ac.il#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075598023","display_name":"Vahab Mirrokni","orcid":"https://orcid.org/0000-0001-6705-5629"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vahab S. Mirrokni","raw_affiliation_strings":["mirrokni@google.com#TAB#"],"affiliations":[{"raw_affiliation_string":"mirrokni@google.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003968234","display_name":"J. Vondr\u00e1k","orcid":"https://orcid.org/0000-0002-4674-0771"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jan Vondr\u00e1k","raw_affiliation_strings":["jvondrak@us.ibm.com#TAB#"],"affiliations":[{"raw_affiliation_string":"jvondrak@us.ibm.com#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013190102"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":20.6801,"has_fulltext":false,"cited_by_count":464,"citation_normalized_percentile":{"value":0.99711036,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"40","issue":"4","first_page":"1133","last_page":"1153"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9890000224113464,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9824000000953674,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9792473912239075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7419695258140564},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7165665626525879},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6776635646820068},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.6634888648986816},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5221845507621765},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48536932468414307},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.4254273772239685},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.39191949367523193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10165190696716309}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.9792473912239075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7419695258140564},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7165665626525879},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6776635646820068},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6634888648986816},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5221845507621765},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48536932468414307},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.4254273772239685},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.39191949367523193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10165190696716309},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/090779346","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090779346","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.121.1148","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.121.1148","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.princeton.edu/~jvondrak/data/submod-max.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.123.5786","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.123.5786","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://theory.csail.mit.edu/~mirrokni/focs07.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.158.4309","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.4309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.wisdom.weizmann.ac.il/~feige/mypapers/FeigeMirrokniVondrak.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.5237","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.5237","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/~jvondrak/data/submod-max-SICOMP.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1680189815","https://openalex.org/W1973315504","https://openalex.org/W1981265575","https://openalex.org/W1985123706","https://openalex.org/W1987550262","https://openalex.org/W1997783781","https://openalex.org/W1998735557","https://openalex.org/W1999032440","https://openalex.org/W2002920311","https://openalex.org/W2033885045","https://openalex.org/W2035575256","https://openalex.org/W2036948347","https://openalex.org/W2062459871","https://openalex.org/W2128059732","https://openalex.org/W2143996311","https://openalex.org/W2806518615"],"related_works":["https://openalex.org/W2382791850","https://openalex.org/W4313349761","https://openalex.org/W2963719189","https://openalex.org/W2775660632","https://openalex.org/W2999146726","https://openalex.org/W2808552933","https://openalex.org/W1773145033","https://openalex.org/W2360385921","https://openalex.org/W2963059222","https://openalex.org/W2923536170"],"abstract_inverted_index":{"Submodular":[0],"maximization":[1],"generalizes":[2],"many":[3],"important":[4],"problems":[5],"including":[6],"Max":[7],"Cut":[8],"in":[9,110,135,184,192],"directed":[10],"and":[11,14,20,64,188],"undirected":[12],"graphs":[13],"hypergraphs,":[15],"certain":[16],"constraint":[17],"satisfaction":[18],"problems,":[19],"maximum":[21],"facility":[22],"location":[23],"problems.":[24],"Unlike":[25],"the":[26,32,45,111,116,156,185,193],"problem":[27,33],"of":[28,34,149,166,177,182,190],"minimizing":[29],"submodular":[30,36,54,72,87,117,142,168],"functions,":[31,88,169],"maximizing":[35,51,70],"functions":[37,143],"is":[38,119,160],"NP-hard.":[39],"In":[40,56,155],"this":[41,136],"paper,":[42],"we":[43,58,89,179],"design":[44],"first":[46],"constant-factor":[47],"approximation":[48],"algorithms":[49,108],"for":[50,69,127,140,151],"nonnegative":[52,71,167],"(non-monotone)":[53],"functions.":[55,73],"particular,":[57],"give":[59],"a":[60,65,78,83,92,96,122,128,138,164,174],"deterministic":[61,104],"local-search":[62],"$\\frac{1}{3}$-approximation":[63],"randomized":[66],"$\\frac{2}{5}$-approximation":[67],"algorithm":[68],"We":[74,132],"also":[75,100],"show":[76,90,133],"that":[77,91,134],"uniformly":[79],"random":[80,93],"set":[81,94,130],"gives":[82,95],"$\\frac{1}{4}$-approximation.":[84],"For":[85],"symmetric":[86,141,186],"$\\frac{1}{2}$-approximation,":[97],"which":[98],"can":[99],"be":[101],"achieved":[102],"by":[103],"local":[105],"search.":[106],"These":[107],"work":[109],"value":[112],"oracle":[113],"model,":[114,137],"where":[115,158],"function":[118],"accessible":[120],"through":[121],"black":[123],"box":[124],"returning":[125],"$f(S)$":[126],"given":[129,161],"S.":[131],"$(\\frac{1}{2}+\\epsilon)$-approximation":[139],"would":[144],"require":[145],"an":[146],"exponential":[147],"number":[148,176],"queries":[150],"any":[152],"fixed":[153],"$\\epsilon>0$.":[154],"model":[157],"f":[159],"explicitly":[162],"(as":[163],"sum":[165],"each":[170],"depending":[171],"only":[172],"on":[173],"constant":[175],"elements),":[178],"prove":[180],"NP-hardness":[181,189],"$(\\frac{5}{6}+\\epsilon)$-approximation":[183],"case":[187],"$(\\frac{3}{4}+\\epsilon)$-approximation":[191],"general":[194],"case.":[195]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":20},{"year":2023,"cited_by_count":28},{"year":2022,"cited_by_count":32},{"year":2021,"cited_by_count":44},{"year":2020,"cited_by_count":48},{"year":2019,"cited_by_count":49},{"year":2018,"cited_by_count":48},{"year":2017,"cited_by_count":39},{"year":2016,"cited_by_count":31},{"year":2015,"cited_by_count":32},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":22},{"year":2012,"cited_by_count":10}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}