{"id":"https://openalex.org/W2167797964","doi":"https://doi.org/10.1145/1024074.1024079","title":"A column approximate minimum degree ordering algorithm","display_name":"A column approximate minimum degree ordering algorithm","publication_year":2004,"publication_date":"2004-09-01","ids":{"openalex":"https://openalex.org/W2167797964","doi":"https://doi.org/10.1145/1024074.1024079","mag":"2167797964"},"language":"en","primary_location":{"id":"doi:10.1145/1024074.1024079","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1024074.1024079","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"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 Mathematical Software","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/A5069178025","display_name":"Timothy A. Davis","orcid":"https://orcid.org/0000-0001-7614-6899"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Timothy A. Davis","raw_affiliation_strings":["University of Florida, Gainesville, FL"],"affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, FL","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108223550","display_name":"John R. Gilbert","orcid":null},"institutions":[{"id":"https://openalex.org/I154570441","display_name":"University of California, Santa Barbara","ror":"https://ror.org/02t274463","country_code":"US","type":"education","lineage":["https://openalex.org/I154570441"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John R. Gilbert","raw_affiliation_strings":["University of California, Santa Barbara, CA"],"affiliations":[{"raw_affiliation_string":"University of California, Santa Barbara, CA","institution_ids":["https://openalex.org/I154570441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013958279","display_name":"Stefan I. Larimore","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":"Stefan I. Larimore","raw_affiliation_strings":["Microsoft, Inc., Redmond, WA"],"affiliations":[{"raw_affiliation_string":"Microsoft, Inc., Redmond, WA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056131016","display_name":"Esmond Ng","orcid":"https://orcid.org/0000-0002-4535-6348"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Esmond G. Ng","raw_affiliation_strings":["Lawrence Berkeley National Laboratory, Berkeley, CA"],"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory, Berkeley, CA","institution_ids":["https://openalex.org/I148283060"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5069178025"],"corresponding_institution_ids":["https://openalex.org/I33213144"],"apc_list":null,"apc_paid":null,"fwci":9.7771,"has_fulltext":false,"cited_by_count":235,"citation_normalized_percentile":{"value":0.98631848,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"30","issue":"3","first_page":"353","last_page":"376"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.7037658095359802},{"id":"https://openalex.org/keywords/gaussian-elimination","display_name":"Gaussian elimination","score":0.6733372211456299},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6513091325759888},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.572600245475769},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5605150461196899},{"id":"https://openalex.org/keywords/column","display_name":"Column (typography)","score":0.5513319373130798},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.5443668961524963},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5023229122161865},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5001487731933594},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4842471778392792},{"id":"https://openalex.org/keywords/minimum-degree-algorithm","display_name":"Minimum degree algorithm","score":0.4817221760749817},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.44447293877601624},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4258948266506195},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3774062395095825},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.364319384098053},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23460900783538818}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.7037658095359802},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.6733372211456299},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6513091325759888},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.572600245475769},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5605150461196899},{"id":"https://openalex.org/C2780551164","wikidata":"https://www.wikidata.org/wiki/Q2306599","display_name":"Column (typography)","level":3,"score":0.5513319373130798},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.5443668961524963},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5023229122161865},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5001487731933594},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4842471778392792},{"id":"https://openalex.org/C46085209","wikidata":"https://www.wikidata.org/wiki/Q17098969","display_name":"Minimum degree algorithm","level":5,"score":0.4817221760749817},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.44447293877601624},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4258948266506195},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3774062395095825},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.364319384098053},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23460900783538818},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1024074.1024079","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1024074.1024079","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"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 Mathematical Software","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":46,"referenced_works":["https://openalex.org/W171063220","https://openalex.org/W1518039036","https://openalex.org/W1531652487","https://openalex.org/W1585892185","https://openalex.org/W1704590117","https://openalex.org/W1965651580","https://openalex.org/W1966561868","https://openalex.org/W1969277007","https://openalex.org/W1971882778","https://openalex.org/W1972859808","https://openalex.org/W1981885118","https://openalex.org/W1989689661","https://openalex.org/W1990474090","https://openalex.org/W2002257715","https://openalex.org/W2007259720","https://openalex.org/W2008859258","https://openalex.org/W2014730252","https://openalex.org/W2020561008","https://openalex.org/W2026121678","https://openalex.org/W2027566319","https://openalex.org/W2028495395","https://openalex.org/W2034197136","https://openalex.org/W2036555554","https://openalex.org/W2038205735","https://openalex.org/W2050324476","https://openalex.org/W2052321453","https://openalex.org/W2063675347","https://openalex.org/W2068543948","https://openalex.org/W2069857942","https://openalex.org/W2074093855","https://openalex.org/W2074965064","https://openalex.org/W2082222857","https://openalex.org/W2083287906","https://openalex.org/W2086648616","https://openalex.org/W2087830284","https://openalex.org/W2088160222","https://openalex.org/W2089437293","https://openalex.org/W2089790965","https://openalex.org/W2091978199","https://openalex.org/W2141025928","https://openalex.org/W2147542748","https://openalex.org/W2151101239","https://openalex.org/W2162810287","https://openalex.org/W2611147814","https://openalex.org/W4249812622","https://openalex.org/W6631119051"],"related_works":["https://openalex.org/W1509943448","https://openalex.org/W2526784484","https://openalex.org/W1987177655","https://openalex.org/W253708524","https://openalex.org/W232494833","https://openalex.org/W2074431240","https://openalex.org/W1545561241","https://openalex.org/W4318710973","https://openalex.org/W2127144731","https://openalex.org/W4224251700"],"abstract_inverted_index":{"Sparse":[0],"Gaussian":[1],"elimination":[2],"with":[3,31,226],"partial":[4,29],"pivoting":[5,30],"computes":[6,223],"the":[7,19,47,55,61,80,99,128,144,184,210,230,233],"factorization":[8,26,130],"PAQ":[9],"=":[10],"LU":[11],"of":[12,50,58,86,91,101,131,147,161,187,232],"a":[13,39,95,112,121,215],"sparse":[14],"matrix":[15],"A":[16,51,117,132,134,136,148,150,166,168,174,188,199],",":[17,43,52,69],"where":[18],"row":[20,32],"ordering":[21,115,123,140,201,217],"P":[22,68,87],"is":[23,36,72,118,178,192,204,207,220],"selected":[24,73],"during":[25],"using":[27],"standard":[28],"interchanges.":[33],"The":[34,63,89],"goal":[35],"to":[37,74,119,151,179],"select":[38],"column":[40,114],"preordering,":[41],"Q":[42,71,92,181],"based":[44,208],"solely":[45],"on":[46,67,79,98,209],"nonzero":[48],"pattern":[49],"that":[53,124],"limits":[54],"worst-case":[56],"number":[57,100],"nonzeros":[59,102,228],"in":[60,103,127,159,229],"factorization.":[62],"fill-in":[64,81,126],"also":[65],"depends":[66],"but":[70,213],"reduce":[75],"an":[76],"upper":[77],"bound":[78],"for":[82,110,116],"any":[83],"subsequent":[84],"choice":[85,90],".":[88,107,135,175],"can":[93,155],"have":[94],"dramatic":[96],"impact":[97],"L":[104],"and":[105,163,222],"U":[106],"One":[108],"scheme":[109],"determining":[111],"good":[113],"compute":[120,180],"symmetric":[122],"reduces":[125],"Cholesky":[129],"T":[133,149,167],"conventional":[137],"minimum":[138],"degree":[139],"algorithm":[141],"would":[142],"require":[143],"sparsity":[145,185],"structure":[146,186],"be":[152,156,170],"computed,":[153],"which":[154],"expensive":[157],"both":[158],"terms":[160],"space":[162],"time":[164],"since":[165],"may":[169],"much":[171],"denser":[172],"than":[173],"An":[176],"alternative":[177],"directly":[182],"from":[183],";":[189],"this":[190],"strategy":[191,212],"used":[193],"by":[194],"MATLAB's":[195],"COLMMD":[196],"preordering":[197],"algorithm.":[198],"new":[200],"algorithm,":[202],"COLAMD,":[203],"presented.":[205],"It":[206],"same":[211],"uses":[214],"better":[216,224],"heuristic.":[218],"COLAMD":[219],"faster":[221],"orderings,":[225],"fewer":[227],"factors":[231],"matrix.":[234]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":31},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":12}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
