{"id":"https://openalex.org/W2346393863","doi":"https://doi.org/10.1145/2856030","title":"Almost Optimal Local Graph Clustering Using Evolving Sets","display_name":"Almost Optimal Local Graph Clustering Using Evolving Sets","publication_year":2016,"publication_date":"2016-05-04","ids":{"openalex":"https://openalex.org/W2346393863","doi":"https://doi.org/10.1145/2856030","mag":"2346393863"},"language":"en","primary_location":{"id":"doi:10.1145/2856030","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2856030","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"Journal of the ACM","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/A5007626895","display_name":"Reid Andersen","orcid":null},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Reid Andersen","raw_affiliation_strings":["Microsoft Corp, Redmond, Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Corp, Redmond, Washington","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017101724","display_name":"Shayan Oveis Gharan","orcid":"https://orcid.org/0000-0002-5504-0849"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shayan Oveis Gharan","raw_affiliation_strings":["University of Washington, Seattle, Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington, Seattle, Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020836845","display_name":"Yuval Peres","orcid":"https://orcid.org/0000-0001-5456-6323"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuval Peres","raw_affiliation_strings":["Microsoft Research, Redmond, Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research, Redmond, Washington","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057752375","display_name":"Luca Trevisan","orcid":"https://orcid.org/0000-0002-6982-8530"},"institutions":[{"id":"https://openalex.org/I134446601","display_name":"Berkeley College","ror":"https://ror.org/02xewxa75","country_code":"US","type":"education","lineage":["https://openalex.org/I134446601"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luca Trevisan","raw_affiliation_strings":["UC Berkeley, Berkeley, California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UC Berkeley, Berkeley, California","institution_ids":["https://openalex.org/I134446601","https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6536,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90260346,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"63","issue":"2","first_page":"1","last_page":"31"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9941999912261963,"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":0.9941999912261963,"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":0.9940999746322632,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9908000230789185,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6213417053222656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6030338406562805},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5837357044219971},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.478074312210083},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.46867331862449646},{"id":"https://openalex.org/keywords/graph-partition","display_name":"Graph partition","score":0.46519601345062256},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4519084692001343},{"id":"https://openalex.org/keywords/conductance","display_name":"Conductance","score":0.449128121137619},{"id":"https://openalex.org/keywords/pagerank","display_name":"PageRank","score":0.4383007884025574},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.42648324370384216},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.41751059889793396},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3764451742172241},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37124013900756836},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35036367177963257},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2182917594909668},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.12048152089118958}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6213417053222656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6030338406562805},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5837357044219971},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.478074312210083},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.46867331862449646},{"id":"https://openalex.org/C48903430","wikidata":"https://www.wikidata.org/wiki/Q491370","display_name":"Graph partition","level":3,"score":0.46519601345062256},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4519084692001343},{"id":"https://openalex.org/C121932024","wikidata":"https://www.wikidata.org/wiki/Q5159376","display_name":"Conductance","level":2,"score":0.449128121137619},{"id":"https://openalex.org/C2779172887","wikidata":"https://www.wikidata.org/wiki/Q184316","display_name":"PageRank","level":2,"score":0.4383007884025574},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.42648324370384216},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.41751059889793396},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3764451742172241},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37124013900756836},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35036367177963257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2182917594909668},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.12048152089118958},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2856030","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2856030","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"Journal of the ACM","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":44,"referenced_works":["https://openalex.org/W42929123","https://openalex.org/W792200198","https://openalex.org/W1507039213","https://openalex.org/W1600293573","https://openalex.org/W1631603072","https://openalex.org/W1910263251","https://openalex.org/W1974633932","https://openalex.org/W1975813814","https://openalex.org/W1984374364","https://openalex.org/W1991556567","https://openalex.org/W1993111701","https://openalex.org/W1999877046","https://openalex.org/W2004879152","https://openalex.org/W2010037144","https://openalex.org/W2019404063","https://openalex.org/W2034331023","https://openalex.org/W2036523948","https://openalex.org/W2045107949","https://openalex.org/W2071708841","https://openalex.org/W2084309732","https://openalex.org/W2086254934","https://openalex.org/W2089703809","https://openalex.org/W2098350988","https://openalex.org/W2103444054","https://openalex.org/W2106285343","https://openalex.org/W2107212520","https://openalex.org/W2111002549","https://openalex.org/W2121947440","https://openalex.org/W2131717044","https://openalex.org/W2132592548","https://openalex.org/W2135512436","https://openalex.org/W2135531856","https://openalex.org/W2138621811","https://openalex.org/W2140432232","https://openalex.org/W2146591355","https://openalex.org/W2148025043","https://openalex.org/W2157071288","https://openalex.org/W2163290928","https://openalex.org/W2163925208","https://openalex.org/W2317597502","https://openalex.org/W2397593282","https://openalex.org/W2952154243","https://openalex.org/W3145128584","https://openalex.org/W4230058301"],"related_works":["https://openalex.org/W2951884240","https://openalex.org/W4297665054","https://openalex.org/W1625594124","https://openalex.org/W1975286263","https://openalex.org/W1588499150","https://openalex.org/W2000539579","https://openalex.org/W2106101949","https://openalex.org/W2888826740","https://openalex.org/W2005018956","https://openalex.org/W2463505734"],"abstract_inverted_index":{"Spectral":[0],"partitioning":[1,34,102,130,312],"is":[2,146,224,247,285,390],"a":[3,18,37,45,53,60,88,126,134,147,191,202,265,320,331,347,354,391,404,431,445,447,455,480],"simple,":[4],"nearly":[5],"linear":[6],"time":[7,275,295,393,488],"algorithm":[8,35,65,131,185,258,296,357,394],"to":[9,66,264,484],"find":[10,104],"sparse":[11,46,105,135],"cuts,":[12],"and":[13,110,114,162,215,330,343,420],"the":[14,22,25,29,64,77,80,92,139,179,206,208,216,219,248,251,260,269,279,282,286,290,293,299,303,308,341,359,485],"Cheeger":[15],"inequalities":[16],"provide":[17],"worst-case":[19],"guarantee":[20,262,301,323],"for":[21,157,174,201,358,396,438],"quality":[23],"of":[24,39,52,76,79,95,152,165,178,193,205,218,250,281,292,324,334,349,362,407,442,444,459,489],"approximation":[26,322,356],"found":[27],"by":[28,48,137,314],"algorithm.":[30],"A":[31,167,183,226,236,242,253],"local":[32,101,129,311],"graph":[33,55],"finds":[36,133,403],"set":[38,81,142,164,192,220,252,405,440],"vertices":[40,96,166,181,443],"with":[41,85,259,297,466],"small":[42],"conductance":[43,170,194],"(i.e.,":[44],"cut)":[47],"adaptively":[49],"exploring":[50],"part":[51],"large":[54],"G":[56,98],",":[57,144,399],"starting":[58,180],"from":[59,454],"specified":[61],"vertex.":[62],"For":[63,365],"be":[67,72],"local,":[68],"its":[69,212],"complexity":[70,214,342],"must":[71],"bounded":[73],"in":[74,97,182,274,278],"terms":[75],"size":[78,280,291],"that":[82,132,156,168,200,221,272,437],"it":[83,222],"outputs,":[84],"at":[86,171,175,468],"most":[87,172],"weak":[89],"dependence":[90],"on":[91,150],"number":[93],"n":[94,232,328,338],".":[99,254,476],"Previous":[100],"algorithms":[103],"cuts":[106],"using":[107],"random":[108,451],"walks":[109],"personalized":[111],"PageRank":[112],"[Spielman":[113],"Teng":[115],"2013;":[116],"Andersen":[117,315],"et":[118,316],"al.":[119,317],"2006].":[120],"In":[121,306],"this":[122],"article,":[123],"we":[124,352,435],"introduce":[125],"simple":[127],"randomized":[128],"cut":[136],"simulating":[138],"volume-biased":[140],"evolving":[141],"process":[143],"which":[145],"Markov":[148,494],"chain":[149],"sets":[151],"vertices.":[153],"We":[154,198],"prove":[155,199,353],"any":[158,163,363,397,439,490],"\u03f5":[159,228,400,418],">":[160,401],"0,":[161,402],"has":[169,319],"\u03c6,":[173],"least":[176,469],"half":[177],"our":[184,350],"will":[186,461],"output":[187,344],"(with":[188],"constant":[189,266],"probability)":[190],"O":[195,325,413,425],"(\u221a\u03c6":[196,326,426],"/\u03f5).":[197],"given":[203],"run":[204],"algorithm,":[207,313],"expected":[209],"ratio":[210,333],"between":[211,340],"computational":[213],"volume":[217,249,408],"outputs":[223],"vol(":[225,235,370,381,409],")":[227,237,246,329,339,376,383,411,419],"\u03c6":[229,335],"-1/2":[230],"polylog(":[231,337],"),":[233],"where":[234],"=":[238],"\u03a3":[239],"v":[240,245],"\u2208":[241],"d":[243],"(":[244,414,427],"This":[255,284,477],"gives":[256],"an":[257],"same":[261,300],"(up":[263],"factor)":[267],"as":[268,302],"Cheeger's":[270,304],"inequality":[271],"runs":[273],"slightly":[276],"superlinear":[277],"output.":[283],"first":[287],"sublinear":[288],"(in":[289],"input)":[294],"almost":[298],"inequality.":[305],"comparison,":[307],"best":[309],"previous":[310],"[2006],":[318],"worse":[321],"log":[327],"larger":[332],"-1":[336],"volume.":[345],"As":[346,430],"by-product":[348],"results,":[351],"bicriteria":[355],"expansion":[360,421],"profile":[361],"graph.":[364],"0":[366],"<":[367],"k":[368,375,385,398,415,428],"\u2264":[369,384,412],"V":[371],")/2,":[372],"let":[373],"\u03c6(":[374,386,422,472],":":[377,380],"min":[378],"S":[379,382,387,406,410,423,441,460,465,473],").":[388],"There":[389],"polynomial":[392],"that,":[395],"1":[416],"+":[417],")\u2264":[424],")/\u03f5).":[429],"new":[432,481],"technical":[433],"tool,":[434],"show":[436],"graph,":[446],"lazy":[448],"t":[449,475],"-step":[450],"walk":[452],"started":[453],"randomly":[456],"chosen":[457],"vertex":[458],"remain":[462],"entirely":[463],"inside":[464],"probability":[467],"(1":[470],"-":[471],")/2)":[474],"itself":[478],"provides":[479],"lower":[482],"bound":[483],"uniform":[486],"mixing":[487],"finite":[491],"state":[492],"reversible":[493],"chain.":[495]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}