{"id":"https://openalex.org/W2979322470","doi":"https://doi.org/10.1142/s1793830919500757","title":"Monotone submodular maximization over the bounded integer lattice with cardinality constraints","display_name":"Monotone submodular maximization over the bounded integer lattice with cardinality constraints","publication_year":2019,"publication_date":"2019-10-07","ids":{"openalex":"https://openalex.org/W2979322470","doi":"https://doi.org/10.1142/s1793830919500757","mag":"2979322470"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830919500757","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500757","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5101836518","display_name":"Lei Lai","orcid":"https://orcid.org/0000-0002-6613-5843"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lei Lai","raw_affiliation_strings":["Shanghai Key Laboratory of PMMP, School of Mathematical Sciences, East China Normal University, Shanghai 200241, P. R. China"],"affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of PMMP, School of Mathematical Sciences, East China Normal University, Shanghai 200241, P. R. China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062834800","display_name":"Qiufen Ni","orcid":"https://orcid.org/0000-0002-0462-9549"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiufen Ni","raw_affiliation_strings":["School of Computer Science, Wuhan University, Wuhan 430070, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Wuhan University, Wuhan 430070, P. R. China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054740983","display_name":"Changhong L\u00fc","orcid":"https://orcid.org/0000-0002-9854-4414"},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changhong Lu","raw_affiliation_strings":["Shanghai Key Laboratory of PMMP, School of Mathematical Sciences, East China Normal University, Shanghai 200241, P. R. China"],"affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory of PMMP, School of Mathematical Sciences, East China Normal University, Shanghai 200241, P. R. China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084572310","display_name":"Chuanhe Huang","orcid":"https://orcid.org/0000-0001-5554-4871"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuanhe Huang","raw_affiliation_strings":["School of Computer Science, Wuhan University, Wuhan 430070, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, Wuhan University, Wuhan 430070, P. R. China","institution_ids":["https://openalex.org/I37461747"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070037321","display_name":"Weili Wu","orcid":"https://orcid.org/0000-0001-8747-6340"},"institutions":[{"id":"https://openalex.org/I162577319","display_name":"The University of Texas at Dallas","ror":"https://ror.org/049emcs32","country_code":"US","type":"education","lineage":["https://openalex.org/I162577319"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weili Wu","raw_affiliation_strings":["Department of Computer Science, University of Texas at Dallas, TX 75080, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Texas at Dallas, TX 75080, USA","institution_ids":["https://openalex.org/I162577319"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101836518"],"corresponding_institution_ids":["https://openalex.org/I66867065"],"apc_list":null,"apc_paid":null,"fwci":0.9699,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.78506831,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"06","first_page":"1950075","last_page":"1950075"},"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":0.9944999814033508,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9916999936103821,"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/submodular-set-function","display_name":"Submodular set function","score":0.9067348837852478},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.691108226776123},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6792327165603638},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6722801923751831},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6561614274978638},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6093252897262573},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5491275787353516},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"Integer lattice","score":0.5357280373573303},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5256744027137756},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.5234167575836182},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5088043808937073},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.4845213294029236},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4542331397533417},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.41430050134658813},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23267841339111328},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15084630250930786}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.9067348837852478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.691108226776123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6792327165603638},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6722801923751831},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6561614274978638},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6093252897262573},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5491275787353516},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.5357280373573303},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5256744027137756},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.5234167575836182},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5088043808937073},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.4845213294029236},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4542331397533417},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.41430050134658813},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23267841339111328},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15084630250930786},{"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/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830919500757","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500757","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-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/W1526762477","https://openalex.org/W1542515633","https://openalex.org/W1576820654","https://openalex.org/W1680189815","https://openalex.org/W1898824936","https://openalex.org/W1987550262","https://openalex.org/W1989801809","https://openalex.org/W1997783781","https://openalex.org/W2036948347","https://openalex.org/W2045492898","https://openalex.org/W2053381548","https://openalex.org/W2098341253","https://openalex.org/W2109974898","https://openalex.org/W2121293983","https://openalex.org/W2132651631","https://openalex.org/W2179494254","https://openalex.org/W2757107770","https://openalex.org/W2889329271","https://openalex.org/W2949112927","https://openalex.org/W2964343703","https://openalex.org/W4231490457","https://openalex.org/W4251076636","https://openalex.org/W4255179538"],"related_works":["https://openalex.org/W2944744777","https://openalex.org/W4321600307","https://openalex.org/W4251076636","https://openalex.org/W2402949237","https://openalex.org/W2964314169","https://openalex.org/W2594118609","https://openalex.org/W2950365512","https://openalex.org/W2735578456","https://openalex.org/W1608444752","https://openalex.org/W3204684126"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,10,54,99,105],"problem":[3,55],"of":[4,56,119],"maximizing":[5,57],"monotone":[6,106],"submodular":[7,23,58,107],"function":[8,59,108],"over":[9,24],"bounded":[11],"integer":[12,25,122],"lattice":[13,26],"with":[14,63],"a":[15,80],"cardinality":[16],"constraint.":[17],"Function":[18],"[Formula:":[19,28,31,45,49,60,65,69,75,82,130,140],"see":[20,29,32,46,50,61,66,70,76,83,131,141],"text]":[21,62,67,132,142],"is":[22,114],"if":[27],"text],":[30,33,47,51],"where":[34],"\u2228":[35],"and":[36,41,48,68,79,136],"\u2227":[37],"represent":[38],"elementwise":[39],"maximum":[40],"minimum,":[42],"respectively.":[43],"Let":[44],"we":[52,103],"study":[53],"constraints":[64],"text].":[71],"A":[72],"random":[73,100,126],"greedy":[74,101,127],"text]-approximation":[77,84],"algorithm":[78,85,128,138],"deterministic":[81,137],"are":[86],"proposed":[87],"in":[88,94],"this":[89],"paper.":[90],"Both":[91],"algorithms":[92],"work":[93],"value":[95,133,143],"oracle":[96,134,144],"model.":[97],"In":[98],"algorithm,":[102],"assume":[104],"satisfies":[109],"diminishing":[110],"return":[111],"property,":[112],"which":[113],"not":[115],"an":[116],"equivalent":[117],"definition":[118],"submodularity":[120],"on":[121],"lattice.":[123],"Additionally,":[124],"our":[125],"makes":[129,139],"queries":[135],"queries.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}