{"id":"https://openalex.org/W1964276725","doi":"https://doi.org/10.1007/s00453-011-9526-1","title":"A Primal-Dual Approximation Algorithm for the Facility Location Problem with Submodular Penalties","display_name":"A Primal-Dual Approximation Algorithm for the Facility Location Problem with Submodular Penalties","publication_year":2011,"publication_date":"2011-05-09","ids":{"openalex":"https://openalex.org/W1964276725","doi":"https://doi.org/10.1007/s00453-011-9526-1","mag":"1964276725"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-011-9526-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-011-9526-1","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","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/A5085441311","display_name":"Donglei Du","orcid":"https://orcid.org/0000-0003-0111-8572"},"institutions":[{"id":"https://openalex.org/I106938459","display_name":"University of New Brunswick","ror":"https://ror.org/05nkf0n29","country_code":"CA","type":"education","lineage":["https://openalex.org/I106938459"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Donglei Du","raw_affiliation_strings":["Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada","University of New Brunswick, Faculty of Business Administration, E3B 5A3, Fredericton, NB, Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada","institution_ids":["https://openalex.org/I106938459"]},{"raw_affiliation_string":"University of New Brunswick, Faculty of Business Administration, E3B 5A3, Fredericton, NB, Canada#TAB#","institution_ids":["https://openalex.org/I106938459"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067427212","display_name":"Ruixing Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruixing Lu","raw_affiliation_strings":["Department of Applied Mathematics, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, P.R. China","Beijing University of Technology, Department of Applied Mathematics, 100 Pingleyuan, Chaoyang District, 100124, Beijing, P.R. China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, P.R. China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"Beijing University of Technology, Department of Applied Mathematics, 100 Pingleyuan, Chaoyang District, 100124, Beijing, P.R. China#TAB#","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100341936","display_name":"Dachuan Xu","orcid":"https://orcid.org/0000-0002-7846-0969"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dachuan Xu","raw_affiliation_strings":["Department of Applied Mathematics, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, P.R. China","Beijing University of Technology, Department of Applied Mathematics, 100 Pingleyuan, Chaoyang District, 100124, Beijing, P.R. China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, P.R. China","institution_ids":["https://openalex.org/I37796252"]},{"raw_affiliation_string":"Beijing University of Technology, Department of Applied Mathematics, 100 Pingleyuan, Chaoyang District, 100124, Beijing, P.R. China#TAB#","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5085441311"],"corresponding_institution_ids":["https://openalex.org/I106938459"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":8.8191,"has_fulltext":false,"cited_by_count":65,"citation_normalized_percentile":{"value":0.98325807,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"63","issue":"1-2","first_page":"191","last_page":"200"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9986000061035156,"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":0.9986000061035156,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.9890000224113464,"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/submodular-set-function","display_name":"Submodular set function","score":0.8526515960693359},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.6812187433242798},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6607780456542969},{"id":"https://openalex.org/keywords/facility-location-problem","display_name":"Facility location problem","score":0.6362930536270142},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6180657148361206},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.5799834132194519},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5056064128875732},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.47029563784599304},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.46039336919784546},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4406570792198181},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4373834431171417},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42450401186943054},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41062888503074646},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35270002484321594},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.34344154596328735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2747717499732971}],"concepts":[{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.8526515960693359},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.6812187433242798},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6607780456542969},{"id":"https://openalex.org/C108005400","wikidata":"https://www.wikidata.org/wiki/Q1305598","display_name":"Facility location problem","level":2,"score":0.6362930536270142},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6180657148361206},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.5799834132194519},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5056064128875732},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.47029563784599304},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.46039336919784546},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4406570792198181},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4373834431171417},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42450401186943054},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41062888503074646},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35270002484321594},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.34344154596328735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2747717499732971},{"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","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/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00453-011-9526-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-011-9526-1","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W113414296","https://openalex.org/W1854155592","https://openalex.org/W1973529814","https://openalex.org/W1978117135","https://openalex.org/W1983553101","https://openalex.org/W1987503114","https://openalex.org/W1988593260","https://openalex.org/W2000500966","https://openalex.org/W2003719999","https://openalex.org/W2011232221","https://openalex.org/W2027016639","https://openalex.org/W2052494364","https://openalex.org/W2053751186","https://openalex.org/W2059862073","https://openalex.org/W2074048915","https://openalex.org/W2076746184","https://openalex.org/W2083653011","https://openalex.org/W2083833523","https://openalex.org/W2101622070","https://openalex.org/W2139841919","https://openalex.org/W2608158342","https://openalex.org/W2769481137","https://openalex.org/W3136436047","https://openalex.org/W4243637616"],"related_works":["https://openalex.org/W2081648281","https://openalex.org/W4256416014","https://openalex.org/W2280623698","https://openalex.org/W2083833523","https://openalex.org/W3143387519","https://openalex.org/W1608444752","https://openalex.org/W2057791178","https://openalex.org/W276709744","https://openalex.org/W1991979416","https://openalex.org/W1973529814"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-02T15:55:50.835912","created_date":"2025-10-10T00:00:00"}
