{"id":"https://openalex.org/W2152781249","doi":"https://doi.org/10.1142/s0129054102001369","title":"ON COMPUTATIONAL COMPLEXITY OF HIERARCHICAL OPTIMIZATION","display_name":"ON COMPUTATIONAL COMPLEXITY OF HIERARCHICAL OPTIMIZATION","publication_year":2002,"publication_date":"2002-10-01","ids":{"openalex":"https://openalex.org/W2152781249","doi":"https://doi.org/10.1142/s0129054102001369","mag":"2152781249"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054102001369","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054102001369","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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":"International Journal of Foundations of Computer Science","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/A5051803761","display_name":"Weijia Jia","orcid":"https://orcid.org/0000-0002-0231-3196"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"WEIJIA JIA","raw_affiliation_strings":["Department of Computer Science,  City University of Hong Kong, Kowloon, R.O.C","Department of Computer Science, City University of Hong Kong, Kowloon, R.O.C"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science,  City University of Hong Kong, Kowloon, R.O.C","institution_ids":[]},{"raw_affiliation_string":"Department of Computer Science, City University of Hong Kong, Kowloon, R.O.C","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070939895","display_name":"Zhibin Sun","orcid":"https://orcid.org/0000-0002-3772-5713"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"ZHIBIN SUN","raw_affiliation_strings":["Zhuhai Applied R&D Centers of City University of Hong Kong Zhuhai, Canton, China"],"affiliations":[{"raw_affiliation_string":"Zhuhai Applied R&D Centers of City University of Hong Kong Zhuhai, Canton, China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051803761"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23305294,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"05","first_page":"667","last_page":"670"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9811000227928162,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.6307322382926941},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5495041608810425},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5449175238609314},{"id":"https://openalex.org/keywords/decision-problem","display_name":"Decision problem","score":0.5120514035224915},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5027120113372803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4921419024467468},{"id":"https://openalex.org/keywords/computational-problem","display_name":"Computational problem","score":0.4340393543243408},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.424777090549469},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.41973668336868286},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34746015071868896},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2592310905456543}],"concepts":[{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.6307322382926941},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5495041608810425},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5449175238609314},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.5120514035224915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5027120113372803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4921419024467468},{"id":"https://openalex.org/C19754495","wikidata":"https://www.wikidata.org/wiki/Q3435924","display_name":"Computational problem","level":2,"score":0.4340393543243408},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.424777090549469},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41973668336868286},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34746015071868896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2592310905456543},{"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},{"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:10.1142/s0129054102001369","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054102001369","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.800000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2023858465","https://openalex.org/W2800745681"],"related_works":["https://openalex.org/W4249702239","https://openalex.org/W2901080149","https://openalex.org/W1512399864","https://openalex.org/W961142965","https://openalex.org/W3203828497","https://openalex.org/W4205799190","https://openalex.org/W2374430960","https://openalex.org/W1589381382","https://openalex.org/W266537895","https://openalex.org/W3105069525"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"the":[3,45,52,71,82,90,93,112,120,124],"computational":[4],"complexity":[5,122],"of":[6,28,54,61,80,89,92,115,123],"a":[7,22,49,59,103],"hierarchic":[8],"optimization":[9],"problem":[10,125],"involving":[11],"in":[12],"several":[13],"players":[14,46],"is":[15,19,30,126],"studied.":[16],"Each":[17],"player":[18,39],"assigned":[20],"with":[21],"linear":[23,62],"objective":[24,113],"function.":[25],"The":[26,85],"set":[27,60],"variables":[29,56,78],"partitioned":[31],"such":[32,57],"that":[33,58,99,119],"each":[34],"subset":[35],"corresponds":[36],"to":[37],"one":[38],"as":[40],"its":[41,76],"decision":[42,50,74,77,91],"variables.":[43],"All":[44],"jointly":[47],"make":[48,95],"on":[51,75],"values":[53],"these":[55],"constraints":[63],"should":[64],"be":[65],"satisfied.":[66],"One":[67],"special":[68],"player,":[69],"called":[70],"leader,":[72,94],"makes":[73],"before":[79],"all":[81],"other":[83],"players.":[84],"rest,":[86],"after":[87],"learnt":[88],"their":[96,100],"choices":[97],"so":[98],"decisions":[101],"form":[102],"Nash":[104],"Equilibrium":[105],"for":[106],"them,":[107],"breaking":[108],"tie":[109],"by":[110],"maximizing":[111],"function":[114],"player.":[116],"We":[117],"show":[118],"exact":[121],"FP":[127],"NP":[128],"-complete.":[129]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}