{"id":"https://openalex.org/W2101511474","doi":"https://doi.org/10.1137/130930352","title":"A Unified Sparse Matrix Data Format for Efficient General Sparse Matrix-Vector Multiplication on Modern Processors with Wide SIMD Units","display_name":"A Unified Sparse Matrix Data Format for Efficient General Sparse Matrix-Vector Multiplication on Modern Processors with Wide SIMD Units","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2101511474","doi":"https://doi.org/10.1137/130930352","mag":"2101511474"},"language":"en","primary_location":{"id":"doi:10.1137/130930352","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130930352","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1307.6209","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038048025","display_name":"Moritz Kreutzer","orcid":"https://orcid.org/0000-0002-7822-9468"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I4210143490","display_name":"Computing Center","ror":"https://ror.org/0557kgc34","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210143490","https://openalex.org/I4210148470"]}],"countries":["DE","RU"],"is_corresponding":false,"raw_author_name":"Moritz Kreutzer","raw_affiliation_strings":["UNIVERSIT \u00c4T ERLANGEN-N \u00dcRNBERG, D-91058 ERLANGEN, GERMANY","ERLANGEN REGIONAL COMPUTING CENTER, FRIEDRICH-ALEXANDER-"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UNIVERSIT \u00c4T ERLANGEN-N \u00dcRNBERG, D-91058 ERLANGEN, GERMANY","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"ERLANGEN REGIONAL COMPUTING CENTER, FRIEDRICH-ALEXANDER-","institution_ids":["https://openalex.org/I4210143490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082552227","display_name":"Georg Hager","orcid":"https://orcid.org/0000-0002-8723-2781"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I4210143490","display_name":"Computing Center","ror":"https://ror.org/0557kgc34","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210143490","https://openalex.org/I4210148470"]}],"countries":["DE","RU"],"is_corresponding":false,"raw_author_name":"Georg Hager","raw_affiliation_strings":["UNIVERSIT \u00c4T ERLANGEN-N \u00dcRNBERG, D-91058 ERLANGEN, GERMANY","ERLANGEN REGIONAL COMPUTING CENTER, FRIEDRICH-ALEXANDER-"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UNIVERSIT \u00c4T ERLANGEN-N \u00dcRNBERG, D-91058 ERLANGEN, GERMANY","institution_ids":["https://openalex.org/I181369854"]},{"raw_affiliation_string":"ERLANGEN REGIONAL COMPUTING CENTER, FRIEDRICH-ALEXANDER-","institution_ids":["https://openalex.org/I4210143490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070209050","display_name":"Gerhard Wellein","orcid":"https://orcid.org/0000-0001-7371-3026"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]},{"id":"https://openalex.org/I4210143490","display_name":"Computing Center","ror":"https://ror.org/0557kgc34","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210143490","https://openalex.org/I4210148470"]}],"countries":["DE","RU"],"is_corresponding":false,"raw_author_name":"Gerhard Wellein","raw_affiliation_strings":["ERLANGEN REGIONAL COMPUTING CENTER, FRIEDRICH-ALEXANDER-","UNIVERSIT \u00c4T ERLANGEN-N \u00dcRNBERG, D-91058 ERLANGEN, GERMANY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ERLANGEN REGIONAL COMPUTING CENTER, FRIEDRICH-ALEXANDER-","institution_ids":["https://openalex.org/I4210143490"]},{"raw_affiliation_string":"UNIVERSIT \u00c4T ERLANGEN-N \u00dcRNBERG, D-91058 ERLANGEN, GERMANY","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056729987","display_name":"Holger Fehske","orcid":"https://orcid.org/0000-0003-2146-8203"},"institutions":[{"id":"https://openalex.org/I36522303","display_name":"Universit\u00e4t Greifswald","ror":"https://ror.org/00r1edq15","country_code":"DE","type":"education","lineage":["https://openalex.org/I36522303"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Holger Fehske","raw_affiliation_strings":["INSTITUT F \u00dcR PHYSIK, ERNST-MORITZ-ARNDT-UNIVERSIT \u00c4T GREIFSWALD, D-17489 GREIFSWALD, GERMANY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INSTITUT F \u00dcR PHYSIK, ERNST-MORITZ-ARNDT-UNIVERSIT \u00c4T GREIFSWALD, D-17489 GREIFSWALD, GERMANY","institution_ids":["https://openalex.org/I36522303"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113506287","display_name":"A. R. Bishop","orcid":"https://orcid.org/0009-0002-4781-387X"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan R. Bishop","raw_affiliation_strings":["THEORY, SIMULATION AND COMPUTATION DIRECTORATE, LOS ALAMOS NA-TIONAL LABORATORY, NEW MEXICO 87545, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"THEORY, SIMULATION AND COMPUTATION DIRECTORATE, LOS ALAMOS NA-TIONAL LABORATORY, NEW MEXICO 87545, USA","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":26.3166,"has_fulltext":false,"cited_by_count":230,"citation_normalized_percentile":{"value":0.99606733,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"36","issue":"5","first_page":"C401","last_page":"C423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9988999962806702,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/simd","display_name":"SIMD","score":0.7908420562744141},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.6972722411155701},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6244196891784668},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5680980682373047},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5615752339363098},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5311658978462219},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5148147940635681},{"id":"https://openalex.org/keywords/vectorization","display_name":"Vectorization (mathematics)","score":0.4457726776599884},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.343833863735199},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24253132939338684},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0912509560585022},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06598249077796936}],"concepts":[{"id":"https://openalex.org/C150552126","wikidata":"https://www.wikidata.org/wiki/Q339387","display_name":"SIMD","level":2,"score":0.7908420562744141},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.6972722411155701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6244196891784668},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5680980682373047},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5615752339363098},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5311658978462219},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5148147940635681},{"id":"https://openalex.org/C41681595","wikidata":"https://www.wikidata.org/wiki/Q7917855","display_name":"Vectorization (mathematics)","level":2,"score":0.4457726776599884},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.343833863735199},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24253132939338684},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0912509560585022},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06598249077796936},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130930352","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130930352","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1307.6209","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.6209","pdf_url":"https://arxiv.org/pdf/1307.6209","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1307.6209","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1307.6209","pdf_url":"https://arxiv.org/pdf/1307.6209","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W158669756","https://openalex.org/W168866822","https://openalex.org/W1505706396","https://openalex.org/W1575701986","https://openalex.org/W1588915715","https://openalex.org/W1776498962","https://openalex.org/W1975116854","https://openalex.org/W1987840949","https://openalex.org/W1990832096","https://openalex.org/W1995649289","https://openalex.org/W2002555321","https://openalex.org/W2023930909","https://openalex.org/W2063186542","https://openalex.org/W2095420020","https://openalex.org/W2097479462","https://openalex.org/W2103877122","https://openalex.org/W2128539477","https://openalex.org/W2128853364","https://openalex.org/W2164904521","https://openalex.org/W2167106676","https://openalex.org/W2518567779","https://openalex.org/W3099744258","https://openalex.org/W3141650078","https://openalex.org/W4230252700"],"related_works":["https://openalex.org/W2566637483","https://openalex.org/W2127324789","https://openalex.org/W3024308452","https://openalex.org/W4244894488","https://openalex.org/W4285390450","https://openalex.org/W2366442643","https://openalex.org/W2090268225","https://openalex.org/W2021715972","https://openalex.org/W2761732860","https://openalex.org/W2766828645"],"abstract_inverted_index":{"Sparse":[0],"matrix-vector":[1],"multiplication":[2],"(spMVM)":[3],"is":[4,33,47,73,192],"the":[5,26,52,77,81,113,168,173,187],"most":[6,69],"time-consuming":[7],"kernel":[8],"in":[9,60,76],"many":[10],"numerical":[11],"algorithms":[12],"and":[13,22,63,107,126,128,144,194],"has":[14],"been":[15],"studied":[16,193],"extensively":[17],"on":[18,132],"all":[19,216,220],"modern":[20],"processor":[21],"accelerator":[23],"architectures.":[24],"However,":[25],"optimal":[27],"sparse":[28,207],"matrix":[29,208],"data":[30,57,94,169],"storage":[31],"format":[32,95],"highly":[34],"hardware-specific,":[35],"which":[36,96,196,210],"could":[37],"become":[38],"an":[39],"obstacle":[40],"when":[41],"using":[42],"heterogeneous":[43],"systems.":[44],"Also,":[45],"it":[46],"as":[48,91],"yet":[49],"unclear":[50],"how":[51],"wide":[53,150],"single":[54],"instruction":[55],"multiple":[56],"(SIMD)":[58],"units":[59],"current":[61],"multi-":[62],"many-core":[64],"processors":[65],"should":[66],"be":[67],"used":[68],"efficiently":[70],"if":[71],"there":[72],"no":[74],"structure":[75],"sparsity":[78],"pattern":[79],"of":[80,88,115,135,152,172,189],"matrix.":[82],"We":[83,111],"suggest":[84],"SELL-C-sigma,":[85],"a":[86,92,133,149,204],"variant":[87],"Sliced":[89],"ELLPACK,":[90],"SIMD-friendly":[93],"combines":[97],"long-standing":[98],"ideas":[99],"from":[100,155],"General":[101],"Purpose":[102],"Graphics":[103],"Processing":[104],"Units":[105],"(GPGPUs)":[106],"vector":[108],"computer":[109],"programming.":[110],"discuss":[112],"advantages":[114],"SELL-C-sigma":[116,174,177],"compared":[117],"to":[118,203],"established":[119],"formats":[120],"like":[121],"Compressed":[122],"Row":[123],"Storage":[124],"(CRS)":[125],"ELLPACK":[127],"show":[129],"its":[130],"suitability":[131],"variety":[134],"hardware":[136,221],"platforms":[137],"(Intel":[138],"Sandy":[139],"Bridge,":[140],"Intel":[141],"Xeon":[142],"Phi":[143],"Nvidia":[145],"Tesla":[146],"K20)":[147],"for":[148,195,215],"range":[151,188],"test":[153,190,217],"matrices":[154,191,218],"different":[156],"application":[157],"areas.":[158],"Using":[159],"appropriate":[160],"performance":[161,184],"models":[162],"we":[163],"develop":[164],"deep":[165],"insight":[166],"into":[167],"transfer":[170],"properties":[171],"spMVM":[175],"kernel.":[176],"comes":[178],"with":[179],"two":[180],"tuning":[181],"parameters":[182],"whose":[183],"impact":[185],"across":[186,219],"reasonable":[197],"choices":[198],"are":[199],"proposed.":[200],"This":[201],"leads":[202],"hardware-independent":[205],"(\"catch-all\")":[206],"format,":[209],"achieves":[211],"very":[212],"high":[213],"efficiency":[214],"platforms.":[222]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":23},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":20},{"year":2021,"cited_by_count":26},{"year":2020,"cited_by_count":26},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":18},{"year":2016,"cited_by_count":23},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":3}],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2016-06-24T00:00:00"}