{"id":"https://openalex.org/W2079250021","doi":"https://doi.org/10.1137/s0895479803386354","title":"On Optimal Reorderings of Sparse Matrices for Parallel Cholesky Factorizations","display_name":"On Optimal Reorderings of Sparse Matrices for Parallel Cholesky Factorizations","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2079250021","doi":"https://doi.org/10.1137/s0895479803386354","mag":"2079250021"},"language":"en","primary_location":{"id":"doi:10.1137/s0895479803386354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803386354","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"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 Matrix Analysis and Applications","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/A5032504698","display_name":"Wen-Yang Lin","orcid":"https://orcid.org/0000-0003-3462-7744"},"institutions":[{"id":"https://openalex.org/I192168892","display_name":"National University of Kaohsiung","ror":"https://ror.org/013zjb662","country_code":"TW","type":"education","lineage":["https://openalex.org/I192168892"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Wen-Yang Lin","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National University of Kaohsiung, Kaohsiung, Taiwan,"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National University of Kaohsiung, Kaohsiung, Taiwan,","institution_ids":["https://openalex.org/I192168892"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061876684","display_name":"Chuen-Liang Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chuen-Liang Chen","raw_affiliation_strings":["Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan,"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan,","institution_ids":["https://openalex.org/I16733864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032504698"],"corresponding_institution_ids":["https://openalex.org/I192168892"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.17148387,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"27","issue":"1","first_page":"24","last_page":"45"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9984999895095825,"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/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.7659041881561279},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7554184198379517},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5709369778633118},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.5560563802719116},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5431787371635437},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5004391670227051},{"id":"https://openalex.org/keywords/minimum-degree-algorithm","display_name":"Minimum degree algorithm","score":0.4891279339790344},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.4751462936401367},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3854162395000458},{"id":"https://openalex.org/keywords/incomplete-cholesky-factorization","display_name":"Incomplete Cholesky factorization","score":0.2964209318161011},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24963265657424927},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09018176794052124}],"concepts":[{"id":"https://openalex.org/C34727166","wikidata":"https://www.wikidata.org/wiki/Q515375","display_name":"Cholesky decomposition","level":3,"score":0.7659041881561279},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7554184198379517},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5709369778633118},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.5560563802719116},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5431787371635437},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5004391670227051},{"id":"https://openalex.org/C46085209","wikidata":"https://www.wikidata.org/wiki/Q17098969","display_name":"Minimum degree algorithm","level":5,"score":0.4891279339790344},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.4751462936401367},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3854162395000458},{"id":"https://openalex.org/C44363057","wikidata":"https://www.wikidata.org/wiki/Q6015160","display_name":"Incomplete Cholesky factorization","level":4,"score":0.2964209318161011},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24963265657424927},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09018176794052124},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895479803386354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895479803386354","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.63.1476","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.1476","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.csie.nuk.edu.tw/~wylin/papers/simax05_lc.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.6100000143051147}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W147544441","https://openalex.org/W1510015875","https://openalex.org/W1980629456","https://openalex.org/W1980946208","https://openalex.org/W1981885118","https://openalex.org/W1993274656","https://openalex.org/W2007903522","https://openalex.org/W2021413160","https://openalex.org/W2025695688","https://openalex.org/W2027140916","https://openalex.org/W2027566319","https://openalex.org/W2029635056","https://openalex.org/W2041700769","https://openalex.org/W2043616552","https://openalex.org/W2051800546","https://openalex.org/W2053427525","https://openalex.org/W2059098138","https://openalex.org/W2063675347","https://openalex.org/W2068683191","https://openalex.org/W2070232376","https://openalex.org/W2070592419","https://openalex.org/W2086648616","https://openalex.org/W2086720083","https://openalex.org/W2122253960","https://openalex.org/W2125720043","https://openalex.org/W2147542748","https://openalex.org/W2152320213","https://openalex.org/W3104001151"],"related_works":["https://openalex.org/W1509943448","https://openalex.org/W2526784484","https://openalex.org/W232494833","https://openalex.org/W2074431240","https://openalex.org/W1987177655","https://openalex.org/W253708524","https://openalex.org/W1545561241","https://openalex.org/W162008856","https://openalex.org/W2313700956","https://openalex.org/W2100843445"],"abstract_inverted_index":{"The":[0],"height":[1,29],"of":[2,113,139,144,149,156,184],"the":[3,10,25,31,52,89,114,121,137,142,147,154,162,169,175],"elimination":[4],"tree":[5],"has":[6,41],"long":[7],"acted":[8],"as":[9,30,69],"only":[11],"criterion":[12,32],"for":[13,21,33],"deriving":[14],"a":[15,57,94],"suitable":[16],"fill-preserving":[17,54],"sparse":[18],"matrix":[19],"ordering":[20,55,96,102,116],"parallel":[22,66,176],"factorization.":[23],"Although":[24],"deficiency":[26],"in":[27,43,65,161,182],"adopting":[28],"all":[34,157],"circumstances":[35],"was":[36],"well":[37],"recognized,":[38],"no":[39],"research":[40],"succeeded":[42],"alleviating":[44],"this":[45,48],"constraint.":[46],"In":[47],"paper,":[49],"we":[50],"extend":[51],"unit-cost":[53],"into":[56],"generalized":[58],"class":[59],"that":[60,79,168],"can":[61,123,172],"adopt":[62],"various":[63,119],"aspects":[64],"factorization,":[67],"such":[68],"computation,":[70],"communication,":[71],"and":[72,77,91,152],"algorithmic":[73],"diversity.":[74],"We":[75,107],"recognize":[76],"show":[78,167],"if":[80],"any":[81],"cost":[82,178],"function":[83],"satisfies":[84],"two":[85],"mandatory":[86],"properties,":[87,93],"called":[88],"independence":[90],"conservation":[92],"greedy":[95],"scheme":[97],"then":[98],"generates":[99],"an":[100,110],"optimal":[101],"with":[103],"minimum":[104],"completion":[105],"cost.":[106],"also":[108],"present":[109],"efficient":[111],"implementation":[112],"proposed":[115,170],"algorithm.":[117],"Incorporating":[118],"techniques,":[120],"complexity":[122],"be":[124],"improved":[125],"from":[126],"O(n":[127],"log":[128,132],"n+e)":[129],"to":[130],"O(q":[131],"q+$\\kappa$),":[133],"where":[134],"n":[135],"denotes":[136],"number":[138,143,148],"nodes,":[140],"e":[141],"edges,":[145],"q":[146],"maximal":[150,158],"cliques,":[151],"$\\kappa$":[153],"sum":[155],"clique":[159],"sizes":[160],"filled":[163],"graph.":[164],"Empirical":[165],"results":[166],"algorithm":[171],"significantly":[173],"reduce":[174],"factorization":[177],"without":[179],"sacrificing":[180],"much":[181],"terms":[183],"time":[185],"efficiency.":[186]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}