{"id":"https://openalex.org/W6969365301","doi":"https://doi.org/10.5525/gla.thesis.83367","title":"Algorithmic aspects of fixed-size coalition formation","display_name":"Algorithmic aspects of fixed-size coalition formation","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W6969365301","doi":"https://doi.org/10.5525/gla.thesis.83367"},"language":"en","primary_location":{"id":"pmh:oai:theses.gla.ac.uk:83367","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401724","display_name":"Enlighten: Theses (The University of Glasgow)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I7882870","host_organization_name":"University of Glasgow","host_organization_lineage":["https://openalex.org/I7882870"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},"type":"dissertation","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5525/gla.thesis.83367","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"McKay, Michael","orcid":"https://orcid.org/0000-0003-1496-7434"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"McKay, Michael","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-1496-7434","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9976999759674072,"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"}},{"id":"https://openalex.org/T11182","display_name":"Auction Theory and Applications","score":0.0005000000237487257,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.0003000000142492354,"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/matching","display_name":"Matching (statistics)","score":0.6202999949455261},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.569100022315979},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5302000045776367},{"id":"https://openalex.org/keywords/rotation-formalisms-in-three-dimensions","display_name":"Rotation formalisms in three dimensions","score":0.4661000072956085},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4300999939441681},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.42179998755455017},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.35440000891685486},{"id":"https://openalex.org/keywords/dichotomy","display_name":"Dichotomy","score":0.35359999537467957}],"concepts":[{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6202999949455261},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.569100022315979},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5302000045776367},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.507099986076355},{"id":"https://openalex.org/C171018156","wikidata":"https://www.wikidata.org/wiki/Q7370306","display_name":"Rotation formalisms in three dimensions","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4226999878883362},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.42179998755455017},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37880000472068787},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3749000132083893},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C59462968","wikidata":"https://www.wikidata.org/wiki/Q10361123","display_name":"Dichotomy","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C146393371","wikidata":"https://www.wikidata.org/wiki/Q620702","display_name":"Stable marriage problem","level":3,"score":0.34299999475479126},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.32600000500679016},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C168031717","wikidata":"https://www.wikidata.org/wiki/Q1530280","display_name":"Balance (ability)","level":2,"score":0.25760000944137573},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25360000133514404},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.2524999976158142},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:theses.gla.ac.uk:83367","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401724","display_name":"Enlighten: Theses (The University of Glasgow)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I7882870","host_organization_name":"University of Glasgow","host_organization_lineage":["https://openalex.org/I7882870"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Thesis"},{"id":"doi:10.5525/gla.thesis.83367","is_oa":true,"landing_page_url":"https://doi.org/10.5525/gla.thesis.83367","pdf_url":null,"source":{"id":"https://openalex.org/S7407050753","display_name":"University of Glasgow","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5525/gla.thesis.83367","is_oa":true,"landing_page_url":"https://doi.org/10.5525/gla.thesis.83367","pdf_url":null,"source":{"id":"https://openalex.org/S7407050753","display_name":"University of Glasgow","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7380529642105103,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,40,144,184,197,232,281,440],"study":[1,391],"algorithmic":[2],"aspects":[3],"of":[4,10,18,30,53,58,65,101,111,119,126,139,164,182,237,251,290,306,331,336,345,355,394,467],"models":[5,23,43,118],"in":[6,44,286,312,324,357,397,421,465],"which":[7,45,69,121,248,287,398],"a":[8,19,28,63,162,206,213,235,260,268,284,315,322,337,343,352,373,402,454],"set":[9,344,354,364],"agents":[11,70,292,333],"is":[12,263,349,382,408,419],"to":[13,115,296,314,334,350,362,444],"be":[14,25,310],"organised":[15],"into":[16],"coalitions":[17,46,335],"fixed":[20,338,374,403,448],"size.":[21,339],"Such":[22],"can":[24,309],"viewed":[26],"as":[27,240,384],"type":[29],"hedonic":[31],"game,":[32,35],"coalition":[33],"formation":[34],"or":[36,369],"multidimensional":[37],"matching":[38,262],"problem.":[39,388],"mostly":[41],"consider":[42,92,136,185,234,267,283,321],"have":[47,71],"size":[48],"three":[49,178],"and":[50,75,95,107,130,153,174,194,204,223,272,300,452,462],"are":[51,60,88,142,151,293],"formalisms":[52],"Three-Dimensional":[54,241],"Roommates":[55],"(3DR).":[56],"Models":[57],"3DR":[59,87,165,238],"characterised":[61],"by":[62,68],"combination":[64],"the":[66,76,82,99,103,137,147,188,288,303,329,347,385,392,399,415,460],"system":[67],"preferences":[72,127,190,246,289],"over":[73],"coalitions,":[74],"solution":[77,220],"concept":[78],"(e.g.":[79],"stability).":[80],"Since":[81],"computational":[83],"problems":[84,150],"associated":[85],"with":[86,98,166,244],"typically":[89],"hard,":[90],"we":[91,135,170,211,266,320,390],"approximate":[93],"solutions":[94],"restricted":[96],"cases,":[97],"aim":[100],"characterising":[102],"boundary":[104],"between":[105],"tractable":[106],"intractable":[108],"variants.":[109],"Part":[110],"our":[112],"contribution":[113],"relates":[114],"two":[116,123],"new":[117],"3DR,":[120],"involve":[122],"existing":[124],"systems":[125],"called":[128],"[B-":[129],"W-preferences].":[131],"In":[132,161],"each":[133],"model,":[134],"existence":[138,222],"matchings":[140,173],"that":[141,146,258,302,327,363,414],"stable.":[143],"show":[145,301],"related":[148,269],"decision":[149],"NP-complete":[152],"devise":[154],"approximation":[155,275,304],"algorithms":[156],"for":[157,177,217,372,410,458,471],"corresponding":[158],"optimisation":[159,270],"problems.":[160],"model":[163],"additively":[167],"separable":[168],"preferences,":[169],"investigate":[171],"stable":[172,261],"envy-free":[175],"matchings,":[176],"successively":[179,218,228],"weaker":[180,219,229],"definitions":[181],"envy-freeness.":[183],"restrictions":[186,203],"on":[187,201,278],"agents\u2019":[189],"including":[191],"symmetric,":[192],"binary,":[193],"ternary":[195],"valuations.":[196],"identify":[198,212],"dichotomies":[199],"based":[200,277],"these":[202,442],"provide":[205,453],"comprehensive":[207],"complexity":[208,456],"classification.":[209],"Interestingly,":[210],"general":[214,380],"trend":[215],"that,":[216],"concepts,":[221],"polynomial-time":[224],"solvability":[225],"hold":[226],"under":[227],"preference":[230],"restrictions.":[231],"also":[233,282],"variant":[236,418],"known":[239,383,409],"Stable":[242],"Matching":[243],"Cyclic":[245],"(3-DSM-CYC),":[247],"has":[249,401],"been":[250],"independent":[252],"interest.":[253],"It":[254,407],"was":[255],"recently":[256],"shown":[257],"finding":[259],"NP-hard,":[264],"so":[265],"problem":[271,323,348,381,396],"present":[273],"an":[274,358,445],"algorithm":[276,308],"serial":[279],"dictatorship.":[280],"situation":[285],"some":[291,297],"sufficiently":[294],"similar":[295],"master":[298],"list,":[299],"ratio":[305],"this":[307,395],"improved":[311],"relation":[313],"specific":[316],"similarity":[317],"measure.":[318],"Finally,":[319],"graph":[325,360,400],"theory":[326],"generalises":[328],"notion":[330],"assigning":[332],"Rather":[340],"than":[341],"organising":[342],"agents,":[346],"find":[351],"maximum-cardinality":[353],"r-cliques":[356],"undirected":[359],"subject":[361],"being":[365],"either":[366],"vertex":[367],"disjoint":[368],"edge":[370],"disjoint,":[371],"integer":[375],"r":[376,411,449,473],"\u2265":[377,435,438,450,474],"3.":[378,475],"This":[379],"Kr-":[386],"packing":[387],"Here":[389],"restriction":[393],"maximum":[404,468],"degree":[405,469],"\u2206.":[406],"=":[412,426,429],"3":[413,427],"vertex-disjoint":[416],"(edge-disjoint)":[417],"solvable":[420],"linear":[422],"time":[423],"if":[424,433],"\u2206":[425,434],"(\u2206":[428,437],"4)":[430],"but":[431,447],"APX-hard":[432],"4":[436],"5).":[439],"generalise":[441],"results":[443],"arbitrary":[446],"3,":[451],"full":[455],"classification":[457],"both":[459],"vertex-":[461],"edge-disjoint":[463],"variants":[464],"graphs":[466],"\u2206,":[470],"all":[472]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
