{"id":"https://openalex.org/W3128258501","doi":"https://doi.org/10.1007/978-981-16-0010-4_8","title":"Nonsubmodular Maximization with Knapsack Constraint via Multilinear Extension","display_name":"Nonsubmodular Maximization with Knapsack Constraint via Multilinear Extension","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3128258501","doi":"https://doi.org/10.1007/978-981-16-0010-4_8","mag":"3128258501"},"language":"en","primary_location":{"id":"doi:10.1007/978-981-16-0010-4_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-981-16-0010-4_8","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5032732960","display_name":"Jiachen Ju","orcid":null},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiachen Ju","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100657775","display_name":"Min Li","orcid":"https://orcid.org/0000-0003-2784-5073"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Li","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015394916","display_name":"Jianxin Liu","orcid":"https://orcid.org/0000-0001-9395-4150"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianxin Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100318513","display_name":"Qian Liu","orcid":"https://orcid.org/0000-0001-6038-4219"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qian Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064833037","display_name":"Yang Zhou","orcid":"https://orcid.org/0000-0001-5692-6281"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Zhou","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People\u2019s Republic of China","institution_ids":["https://openalex.org/I28006308"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People's Republic of China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032732960"],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04820038,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"81","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987999796867371,"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":0.9987999796867371,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9872000217437744,"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"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9800999760627747,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/knapsack-problem","display_name":"Knapsack problem","score":0.8457391262054443},{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.7140878438949585},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6625339984893799},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6608070731163025},{"id":"https://openalex.org/keywords/submodular-set-function","display_name":"Submodular set function","score":0.6517552137374878},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.5648157000541687},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5601349472999573},{"id":"https://openalex.org/keywords/rounding","display_name":"Rounding","score":0.48882123827934265},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4665021300315857},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45685580372810364},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.42436468601226807},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4075685143470764},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2542107105255127},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1754918396472931},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13981252908706665},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13121798634529114},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07462736964225769}],"concepts":[{"id":"https://openalex.org/C113138325","wikidata":"https://www.wikidata.org/wiki/Q864457","display_name":"Knapsack problem","level":2,"score":0.8457391262054443},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.7140878438949585},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6625339984893799},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6608070731163025},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.6517552137374878},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.5648157000541687},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5601349472999573},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.48882123827934265},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4665021300315857},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45685580372810364},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.42436468601226807},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4075685143470764},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2542107105255127},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1754918396472931},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13981252908706665},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13121798634529114},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07462736964225769},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-981-16-0010-4_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-981-16-0010-4_8","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W2012882533","https://openalex.org/W2033885045","https://openalex.org/W2039811877","https://openalex.org/W2094067695","https://openalex.org/W2129866531","https://openalex.org/W2130956934","https://openalex.org/W2148849245","https://openalex.org/W2252172643","https://openalex.org/W2949203029","https://openalex.org/W2955556456","https://openalex.org/W2963793685","https://openalex.org/W2964501918","https://openalex.org/W2968895370","https://openalex.org/W3138381145","https://openalex.org/W3144959161","https://openalex.org/W3207262409","https://openalex.org/W4231490457"],"related_works":["https://openalex.org/W2357796514","https://openalex.org/W2393014972","https://openalex.org/W2357595179","https://openalex.org/W2351136238","https://openalex.org/W2402949237","https://openalex.org/W2891162720","https://openalex.org/W2594118609","https://openalex.org/W3171554204","https://openalex.org/W2765425000","https://openalex.org/W3204684126"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
