{"id":"https://openalex.org/W2074167246","doi":"https://doi.org/10.1145/1367064.1367075","title":"Clustering, community partition and disjoint spanning trees","display_name":"Clustering, community partition and disjoint spanning trees","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2074167246","doi":"https://doi.org/10.1145/1367064.1367075","mag":"2074167246"},"language":"en","primary_location":{"id":"doi:10.1145/1367064.1367075","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1367064.1367075","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","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/A5064703404","display_name":"Cun\u2010Quan Zhang","orcid":"https://orcid.org/0000-0001-5583-4481"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cun-Quan Zhang","raw_affiliation_strings":["West Virginia University, Morgantown, WV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"West Virginia University, Morgantown, WV","institution_ids":["https://openalex.org/I12097938"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059437391","display_name":"Yongbin Ou","orcid":"https://orcid.org/0000-0002-4347-7146"},"institutions":[{"id":"https://openalex.org/I12097938","display_name":"West Virginia University","ror":"https://ror.org/011vxgd24","country_code":"US","type":"education","lineage":["https://openalex.org/I12097938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yongbin Ou","raw_affiliation_strings":["West Virginia University, Morgantown, WV"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"West Virginia University, Morgantown, WV","institution_ids":["https://openalex.org/I12097938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.13760259,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"4","issue":"3","first_page":"1","last_page":"26"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.7674989700317383},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.649871826171875},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.5786116123199463},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5505188703536987},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4936865270137787},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.491013765335083},{"id":"https://openalex.org/keywords/distance-hereditary-graph","display_name":"Distance-hereditary graph","score":0.4320601224899292},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.4296432137489319},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.42794856429100037},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.4262222349643707},{"id":"https://openalex.org/keywords/factor-critical-graph","display_name":"Factor-critical graph","score":0.4193102717399597},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3903258144855499},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.3033773601055145},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.28192949295043945}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7674989700317383},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.649871826171875},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.5786116123199463},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5505188703536987},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4936865270137787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.491013765335083},{"id":"https://openalex.org/C147792647","wikidata":"https://www.wikidata.org/wiki/Q5282847","display_name":"Distance-hereditary graph","level":5,"score":0.4320601224899292},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.4296432137489319},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.42794856429100037},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.4262222349643707},{"id":"https://openalex.org/C36038622","wikidata":"https://www.wikidata.org/wiki/Q5428703","display_name":"Factor-critical graph","level":5,"score":0.4193102717399597},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3903258144855499},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3033773601055145},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.28192949295043945},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1367064.1367075","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1367064.1367075","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6541373138","display_name":null,"funder_award_id":"(MDA904-01-1-0022)","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W86527203","https://openalex.org/W95719993","https://openalex.org/W950821216","https://openalex.org/W1501500081","https://openalex.org/W1501730368","https://openalex.org/W1563416066","https://openalex.org/W1611682757","https://openalex.org/W1651093245","https://openalex.org/W1948612123","https://openalex.org/W1971421925","https://openalex.org/W1971788485","https://openalex.org/W1971937094","https://openalex.org/W1990368529","https://openalex.org/W1992419399","https://openalex.org/W1998871699","https://openalex.org/W1999668761","https://openalex.org/W2002041442","https://openalex.org/W2012287357","https://openalex.org/W2038518475","https://openalex.org/W2038920443","https://openalex.org/W2042706982","https://openalex.org/W2047555270","https://openalex.org/W2048239613","https://openalex.org/W2058858486","https://openalex.org/W2062931369","https://openalex.org/W2065320942","https://openalex.org/W2079522169","https://openalex.org/W2080656989","https://openalex.org/W2090359754","https://openalex.org/W2092348181","https://openalex.org/W2110898430","https://openalex.org/W2113076747","https://openalex.org/W2121182136","https://openalex.org/W2122111042","https://openalex.org/W2123720352","https://openalex.org/W2124608963","https://openalex.org/W2127218421","https://openalex.org/W2127284416","https://openalex.org/W2140190241","https://openalex.org/W2148606255","https://openalex.org/W2157682389","https://openalex.org/W2165298438","https://openalex.org/W2913066018","https://openalex.org/W2913668833","https://openalex.org/W3190326073","https://openalex.org/W4233105605","https://openalex.org/W4247278211","https://openalex.org/W6633697183","https://openalex.org/W6660056414"],"related_works":["https://openalex.org/W2953496651","https://openalex.org/W2393701947","https://openalex.org/W3208942821","https://openalex.org/W2886672068","https://openalex.org/W4285101991","https://openalex.org/W3173082423","https://openalex.org/W2404212820","https://openalex.org/W2978860557","https://openalex.org/W4310153179","https://openalex.org/W2124956389"],"abstract_inverted_index":{"Clustering":[0],"method":[1,195],"is":[2,17,32,65,95,113,134,141,156,179,196,242],"one":[3,197],"of":[4,20,57,63,102,106,123,132,145,167,176,198,236],"the":[5,18,66,93,103,114,216],"most":[6],"important":[7],"tools":[8],"in":[9,34,158],"statistics.":[10],"In":[11],"a":[12,48,55,126,135,142,223,237],"graph":[13,30,49,115],"theory":[14],"model,":[15],"clustering":[16,201],"process":[19],"finding":[21,232],"all":[22,98,163,245],"dense":[23],"subgraphs.":[24],"A":[25,129],"mathematically":[26,205],"well-defined":[27],"measure":[28],"for":[29,231,248],"density":[31,62,149],"introduced":[33],"this":[35,159,177,225],"article":[36],"as":[37],"follows.":[38],"Let":[39],"G":[40,58,133,146,171,187],"=":[41],"(":[42,77,83,186],"V":[43,82,185],",":[44,108],"E":[45,76],")":[46],"be":[47,54,229],"(or":[50],"multi-graph)":[51],"and":[52,109,212],"H":[53,64,78,84,107,110,118,131,140],"subgraph":[56,130,144],".":[59,153,172],"The":[60,173,239],"dynamic":[61,148],"greatest":[67],"integer":[68],"k":[69,91,137,152],"such":[70],"that":[71,203],"min":[72],"\u2200":[73],"P":[74,80,86,101,112,124],"{|":[75],"/":[79,85,111],")|/|":[81],")|":[87,188],"\u2212":[88],"1}":[89],"&gt;":[90],"where":[92],"minimum":[94],"taken":[96],"over":[97],"possible":[99],"partitions":[100],"vertex":[104],"set":[105],"obtained":[116],"from":[117],"by":[119,182,208],"contracting":[120],"each":[121],"part":[122],"into":[125],"single":[127],"vertex.":[128],"level-":[136,164],"community":[138],"if":[139],"maximal":[143],"with":[147,219],"at":[150],"least":[151],"An":[154],"algorithm":[155,178,226],"designed":[157],"paper":[160],"to":[161,214],"detect":[162],"h":[165,190],"communities":[166],"an":[168],"input":[169],"multi-graph":[170],"worst-case":[174,240],"complexity":[175,241],"upper":[180],"bounded":[181],"O":[183],"(|":[184],"2":[189,191],").":[192],"This":[193],"new":[194],"few":[199],"available":[200],"methods":[202],"are":[204],"well-defined,":[206],"supported":[207],"rigorous":[209],"mathematical":[210],"proof":[211],"able":[213],"achieve":[215],"optimization":[217],"goal":[218],"polynomial":[220],"complexity.":[221],"As":[222],"byproduct,":[224],"also":[227],"can":[228],"applied":[230],"edge-disjoint":[233],"spanning":[234],"trees":[235],"multi-graph.":[238],"lower":[243],"than":[244],"known":[246],"algorithms":[247],"multi-graphs.":[249]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
