{"id":"https://openalex.org/W2948499415","doi":"https://doi.org/10.1137/18m1217152","title":"Metric-Constrained Optimization for Graph Clustering Algorithms","display_name":"Metric-Constrained Optimization for Graph Clustering Algorithms","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2948499415","doi":"https://doi.org/10.1137/18m1217152","mag":"2948499415"},"language":"en","primary_location":{"id":"doi:10.1137/18m1217152","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1217152","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1217152","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1217152","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046315164","display_name":"Nate Veldt","orcid":"https://orcid.org/0000-0002-0117-3304"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Nate Veldt","raw_affiliation_strings":["Purdue Univ., West Lafayette#TAB#"],"affiliations":[{"raw_affiliation_string":"Purdue Univ., West Lafayette#TAB#","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084102378","display_name":"David F. Gleich","orcid":"https://orcid.org/0000-0002-8107-6474"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David F. Gleich","raw_affiliation_strings":["Purdue Univ., West Lafayette#TAB#"],"affiliations":[{"raw_affiliation_string":"Purdue Univ., West Lafayette#TAB#","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087794199","display_name":"Anthony Wirth","orcid":"https://orcid.org/0000-0003-3746-6704"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Anthony Wirth","raw_affiliation_strings":["University of Melbourne"],"affiliations":[{"raw_affiliation_string":"University of Melbourne","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037774037","display_name":"James Saunderson","orcid":"https://orcid.org/0000-0002-5456-0180"},"institutions":[{"id":"https://openalex.org/I4210116219","display_name":"Engineering Systems (United States)","ror":"https://ror.org/02qg60849","country_code":"US","type":"company","lineage":["https://openalex.org/I4210116219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Saunderson","raw_affiliation_strings":["Electrical and Computer Systems Engineering"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Systems Engineering","institution_ids":["https://openalex.org/I4210116219"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046315164"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":1.9939,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.87388056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"1","issue":"2","first_page":"333","last_page":"355"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9793999791145325,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.967199981212616,"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/cluster-analysis","display_name":"Cluster analysis","score":0.6935552358627319},{"id":"https://openalex.org/keywords/constrained-clustering","display_name":"Constrained clustering","score":0.5632815361022949},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5324004292488098},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.523988664150238},{"id":"https://openalex.org/keywords/correlation-clustering","display_name":"Correlation clustering","score":0.5072169303894043},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5010178089141846},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.4846654236316681},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4677296578884125},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.46720072627067566},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4515978693962097},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4192807972431183},{"id":"https://openalex.org/keywords/linear-programming-relaxation","display_name":"Linear programming relaxation","score":0.41450488567352295},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36643120646476746},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36283978819847107},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.20848879218101501},{"id":"https://openalex.org/keywords/canopy-clustering-algorithm","display_name":"Canopy clustering algorithm","score":0.20024073123931885},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17308813333511353}],"concepts":[{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.6935552358627319},{"id":"https://openalex.org/C27964816","wikidata":"https://www.wikidata.org/wiki/Q5164359","display_name":"Constrained clustering","level":5,"score":0.5632815361022949},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5324004292488098},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.523988664150238},{"id":"https://openalex.org/C94641424","wikidata":"https://www.wikidata.org/wiki/Q5172845","display_name":"Correlation clustering","level":3,"score":0.5072169303894043},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5010178089141846},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.4846654236316681},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4677296578884125},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.46720072627067566},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4515978693962097},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4192807972431183},{"id":"https://openalex.org/C25360446","wikidata":"https://www.wikidata.org/wiki/Q1512771","display_name":"Linear programming relaxation","level":3,"score":0.41450488567352295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36643120646476746},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36283978819847107},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20848879218101501},{"id":"https://openalex.org/C104047586","wikidata":"https://www.wikidata.org/wiki/Q5033439","display_name":"Canopy clustering algorithm","level":4,"score":0.20024073123931885},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17308813333511353},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1217152","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1217152","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1217152","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1137/18m1217152","is_oa":true,"landing_page_url":"https://doi.org/10.1137/18m1217152","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/18M1217152","source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1739869781","display_name":null,"funder_award_id":"CCF-0939370","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3548042388","display_name":null,"funder_award_id":"CCF-1149756","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4114895836","display_name":null,"funder_award_id":"IIS-1422918","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6202820553","display_name":null,"funder_award_id":"DE-SC0014543","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320320974","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2948499415.pdf","grobid_xml":"https://content.openalex.org/works/W2948499415.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W132912941","https://openalex.org/W205960364","https://openalex.org/W379260703","https://openalex.org/W1440788545","https://openalex.org/W1601412462","https://openalex.org/W1881624953","https://openalex.org/W1958024236","https://openalex.org/W1974451927","https://openalex.org/W1974906551","https://openalex.org/W1976576957","https://openalex.org/W1976936504","https://openalex.org/W1982119153","https://openalex.org/W1985142495","https://openalex.org/W1986245501","https://openalex.org/W1988153470","https://openalex.org/W2017732166","https://openalex.org/W2018711500","https://openalex.org/W2022393739","https://openalex.org/W2024778356","https://openalex.org/W2035080386","https://openalex.org/W2045387243","https://openalex.org/W2047609571","https://openalex.org/W2050958540","https://openalex.org/W2054821093","https://openalex.org/W2057504236","https://openalex.org/W2059448930","https://openalex.org/W2077742312","https://openalex.org/W2088844265","https://openalex.org/W2091858563","https://openalex.org/W2095293504","https://openalex.org/W2102338614","https://openalex.org/W2105419023","https://openalex.org/W2131681506","https://openalex.org/W2146081992","https://openalex.org/W2150148016","https://openalex.org/W2173145870","https://openalex.org/W2247411266","https://openalex.org/W2252324212","https://openalex.org/W2502264282","https://openalex.org/W2567383059","https://openalex.org/W2788340096","https://openalex.org/W2803630713","https://openalex.org/W2805765082","https://openalex.org/W2914959486","https://openalex.org/W2963643331","https://openalex.org/W3099768174","https://openalex.org/W3104252707"],"related_works":["https://openalex.org/W2107689258","https://openalex.org/W4205854323","https://openalex.org/W2115855742","https://openalex.org/W2059496069","https://openalex.org/W3149578574","https://openalex.org/W4387578030","https://openalex.org/W3146523624","https://openalex.org/W2895393216","https://openalex.org/W2378280103","https://openalex.org/W2951567704"],"abstract_inverted_index":{"We":[0,57,86,111,139],"outline":[1],"a":[2,73,77,89,102],"new":[3],"approach":[4,120],"for":[5,41,92,108,117,125],"solving":[6,147],"linear":[7,62,94],"programming":[8,63],"relaxations":[9,32,148],"of":[10,65,76,143,149],"NP-hard":[11],"graph":[12,127],"clustering":[13,42,68,128],"problems":[14,151],"that":[15,28,60],"enforce":[16],"triangle":[17],"inequality":[18],"constraints":[19],"on":[20],"output":[21],"variables.":[22],"Extensive":[23],"previous":[24],"research":[25],"has":[26],"shown":[27],"solutions":[29],"to":[30,36,52,72,121,154],"these":[31,45,150],"can":[33],"be":[34],"used":[35],"obtain":[37],"good":[38],"approximation":[39,115],"algorithms":[40],"objectives.":[43],"However,":[44],"are":[46],"rarely":[47],"solved":[48],"in":[49,80],"practice":[50],"due":[51],"their":[53],"high":[54],"memory":[55],"requirements.":[56],"first":[58],"prove":[59],"the":[61,66,141],"relaxation":[64],"correlation":[67,137],"objective":[69],"is":[70],"equivalent":[71],"special":[74],"case":[75],"well-known":[78],"problem":[79],"machine":[81],"learning":[82],"called":[83],"metric":[84,109],"nearness.":[85,110],"then":[87],"develop":[88],"general":[90],"solver":[91],"metric-constrained":[93],"and":[95,100,136,157],"quadratic":[96],"programs":[97],"by":[98,146],"generalizing":[99],"improving":[101],"simple":[103],"projection":[104],"algorithm,":[105],"originally":[106],"developed":[107],"give":[112],"several":[113],"novel":[114],"guarantees":[116],"using":[118],"our":[119,144],"find":[122],"lower":[123],"bounds":[124],"challenging":[126],"tasks":[129],"such":[130],"as":[131],"sparsest":[132],"cut,":[133],"maximum":[134],"modularity,":[135],"clustering.":[138],"demonstrate":[140],"power":[142],"framework":[145],"involving":[152],"up":[153],"$10^7$":[155],"variables":[156],"$10^{11}$":[158],"constraints.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}