{"id":"https://openalex.org/W2026317193","doi":"https://doi.org/10.1080/10637199508915506","title":"THE MAXIMUM WEIGHT PERFECT MATCHING PROBLEM FOR COMPLETE WEIGHTED GRAPHS IS IN PC\u2217\u2020","display_name":"THE MAXIMUM WEIGHT PERFECT MATCHING PROBLEM FOR COMPLETE WEIGHTED GRAPHS IS IN PC\u2217\u2020","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2026317193","doi":"https://doi.org/10.1080/10637199508915506","mag":"2026317193"},"language":"en","primary_location":{"id":"doi:10.1080/10637199508915506","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10637199508915506","pdf_url":null,"source":{"id":"https://openalex.org/S89732838","display_name":"Parallel algorithms and applications","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel 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/A5083232449","display_name":"C.N.K. Osiakwan","orcid":null},"institutions":[{"id":"https://openalex.org/I176714629","display_name":"Bell (Canada)","ror":"https://ror.org/00xdg8m59","country_code":"CA","type":"company","lineage":["https://openalex.org/I176714629"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"CONSTANTINE N.K. OSIAKWAN","raw_affiliation_strings":["Bell Northern Research , 3500 Carling Avenue, Ottawa, Ontario, Canada , K1Y 4H7"],"affiliations":[{"raw_affiliation_string":"Bell Northern Research , 3500 Carling Avenue, Ottawa, Ontario, Canada , K1Y 4H7","institution_ids":["https://openalex.org/I176714629"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041804050","display_name":"Selim G. Akl","orcid":"https://orcid.org/0000-0002-5742-9356"},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"SELIM G. AKL","raw_affiliation_strings":["Computing and Information Science , Queen's University , Kingston, Ontario, Canada , K7L 3N6","Computing and Information Science Queen's University Kingston, Ontario, Canada K7L 3N6"],"affiliations":[{"raw_affiliation_string":"Computing and Information Science , Queen's University , Kingston, Ontario, Canada , K7L 3N6","institution_ids":["https://openalex.org/I204722609"]},{"raw_affiliation_string":"Computing and Information Science Queen's University Kingston, Ontario, Canada K7L 3N6","institution_ids":["https://openalex.org/I204722609"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5083232449"],"corresponding_institution_ids":["https://openalex.org/I176714629"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.15209966,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"6","issue":"2-3","first_page":"143","last_page":"166"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9965000152587891,"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/T12288","display_name":"Optimization and Search Problems","score":0.9925000071525574,"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/combinatorics","display_name":"Combinatorics","score":0.7540246248245239},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6980794668197632},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6162179708480835},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.5238128900527954},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4754749834537506},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43730974197387695},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.433095246553421},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.424483060836792},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3557584881782532}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7540246248245239},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6980794668197632},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6162179708480835},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.5238128900527954},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4754749834537506},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43730974197387695},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.433095246553421},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.424483060836792},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3557584881782532},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10637199508915506","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10637199508915506","pdf_url":null,"source":{"id":"https://openalex.org/S89732838","display_name":"Parallel algorithms and applications","issn_l":"1026-7689","issn":["1026-7689","1029-032X","1063-7192"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Parallel 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":38,"referenced_works":["https://openalex.org/W38097373","https://openalex.org/W131807657","https://openalex.org/W140737195","https://openalex.org/W1558316751","https://openalex.org/W1919479762","https://openalex.org/W1977041160","https://openalex.org/W1979641885","https://openalex.org/W1981234161","https://openalex.org/W1992060486","https://openalex.org/W2011039300","https://openalex.org/W2011591414","https://openalex.org/W2028365850","https://openalex.org/W2037752639","https://openalex.org/W2040326319","https://openalex.org/W2040699536","https://openalex.org/W2041786457","https://openalex.org/W2049337025","https://openalex.org/W2054420170","https://openalex.org/W2063301486","https://openalex.org/W2064284095","https://openalex.org/W2074276908","https://openalex.org/W2074499935","https://openalex.org/W2078629151","https://openalex.org/W2081385108","https://openalex.org/W2088141885","https://openalex.org/W2090133546","https://openalex.org/W2109560070","https://openalex.org/W2125690626","https://openalex.org/W2130566259","https://openalex.org/W2139932807","https://openalex.org/W2159008239","https://openalex.org/W2427045451","https://openalex.org/W2561675875","https://openalex.org/W2610729871","https://openalex.org/W2799004609","https://openalex.org/W4210697874","https://openalex.org/W4213214460","https://openalex.org/W4241108585"],"related_works":["https://openalex.org/W2046435967","https://openalex.org/W4231775656","https://openalex.org/W1972035260","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W2354191502","https://openalex.org/W1972225038","https://openalex.org/W3134658850","https://openalex.org/W2355938171","https://openalex.org/W2780079842"],"abstract_inverted_index":{"A":[0,27,77],"matching":[1,31,40,55,144,159,234,281],"M":[2,24],"of":[3,12,15,32,41,47,50,79,174,193,200,219,243,265],"a":[4,10,33,38,94,161,262],"graph":[5,36,43],"G":[6],"=":[7],"(V,E)":[8],"is":[9,37,56,116,128,167,190,197,239,268],"subset":[11],"the":[13,42,45,48,51,54,91,123,141,170,191,198,203,214,230,241,259,269,278],"set":[14],"edges":[16,22,52],"E":[17],"such":[18],"that":[19,63,130,136,229],"no":[20],"two":[21],"in":[23,53,90,103,160,179,202,240],"are":[25,59,74],"adjacent.":[26],"maximum":[28,70,84,100,142,156,231,279],"weight":[29,71,85,101,143,157,232,280],"(perfect)":[30,39],"(complete)":[34],"weighted":[35,163],"where":[44,188],"sum":[46],"weights":[49],"maximum.":[57],"There":[58],"efficient":[60],"sequential":[61,216],"algorithms":[62,82],"use":[64],"linear":[65],"programming":[66],"(LP)":[67],"for":[68,83,98,111,155,169,185,225,236,248,277],"computing":[69,99],"matchings.":[72],"These":[73],"primal-dual":[75],"algorithms.":[76],"number":[78,192,199,264],"randomized":[80],"parallel":[81,96,124,153,175,253,274],"matchings":[86,102],"have":[87],"also":[88],"appeared":[89],"literature.":[92],"Finding":[93],"deterministic":[95,271],"algorithm":[97,135,154,166,206,254,275],"complete":[104,162,237,284],"graphs":[105,238],"has":[106],"been":[107],"an":[108,133,151,208,250],"open":[109],"problem":[110,235,282],"some":[112],"time.":[113],"Since":[114],"LP":[115,138],"known":[117],"to":[118,139,213],"be":[119,256],"P-complete,":[120],"then,":[121],"by":[122],"computation":[125],"thesis,":[126],"it":[127],"unlikely":[129],"there":[131],"exists":[132],"NC":[134],"uses":[137],"solve":[140],"problem.":[145],"In":[146],"this":[147],"paper,":[148],"we":[149],"present":[150],"LP-based":[152,217],"perfect":[158,233],"graph.":[164,204],"The":[165],"designed":[168,257,276],"EREW":[171],"PRAM":[172,260],"model":[173],"computation,":[176],"and":[177,195],"runs":[178],"O(n3/p":[180],"+":[181],"n2":[182],"logn)":[183],"time":[184],"p":[186,189],"\u2264n,":[187],"processors":[194],"n":[196],"vertices":[201],"This":[205,227,267],"provides":[207],"optimal":[209,251,272],"speedup":[210,252,273],"with":[211],"respect":[212],"O(n3)":[215],"solution":[218],"Gabow":[220],"[18]":[221],"or":[222],"Lawler":[223],"[28],":[224],"p\u2264n/logn.":[226],"shows":[228],"class":[242],"problems":[244],"(known":[245],"as":[246],"PC\u2217)":[247],"which":[249],"can":[255],"on":[258,283],"using":[261],"polynomial":[263],"processors.":[266],"first":[270],"graphs.":[285]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}