{"id":"https://openalex.org/W2043670592","doi":"https://doi.org/10.1145/1077464.1077466","title":"Fast sparse matrix multiplication","display_name":"Fast sparse matrix multiplication","publication_year":2005,"publication_date":"2005-07-01","ids":{"openalex":"https://openalex.org/W2043670592","doi":"https://doi.org/10.1145/1077464.1077466","mag":"2043670592"},"language":"en","primary_location":{"id":"doi:10.1145/1077464.1077466","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1077464.1077466","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"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 Algorithms","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/A5026016357","display_name":"Raphael Yuster","orcid":"https://orcid.org/0000-0001-7550-6506"},"institutions":[{"id":"https://openalex.org/I91203450","display_name":"University of Haifa","ror":"https://ror.org/02f009v59","country_code":"IL","type":"education","lineage":["https://openalex.org/I91203450"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Raphael Yuster","raw_affiliation_strings":["University of Haifa, Haifa, Israel",", University of Haifa, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Haifa, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]},{"raw_affiliation_string":", University of Haifa, Haifa, Israel","institution_ids":["https://openalex.org/I91203450"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005525211","display_name":"Uri Zwick","orcid":"https://orcid.org/0000-0002-7638-7710"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Uri Zwick","raw_affiliation_strings":["Tel-Aviv University, Tel-Aviv, Israel","Tel Aviv University, Tel Aviv, Israel,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel-Aviv University, Tel-Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, Tel Aviv, Israel,","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3188,"has_fulltext":false,"cited_by_count":258,"citation_normalized_percentile":{"value":0.97306019,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"1","issue":"1","first_page":"2","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9983999729156494,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9983999729156494,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.8236707448959351},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.7615882158279419},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.7610487341880798},{"id":"https://openalex.org/keywords/strassen-algorithm","display_name":"Strassen algorithm","score":0.6775265336036682},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.613096296787262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.599371075630188},{"id":"https://openalex.org/keywords/freivalds-algorithm","display_name":"Freivalds' algorithm","score":0.510410487651825},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5017185211181641},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.49557340145111084},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46408650279045105},{"id":"https://openalex.org/keywords/integer-matrix","display_name":"Integer matrix","score":0.43256378173828125},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4139842092990875},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4010123014450073},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3895268142223358},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.19409751892089844},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.09282064437866211},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07023313641548157},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.05872923135757446}],"concepts":[{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.8236707448959351},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.7615882158279419},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7610487341880798},{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.6775265336036682},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.613096296787262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.599371075630188},{"id":"https://openalex.org/C38506071","wikidata":"https://www.wikidata.org/wiki/Q6522941","display_name":"Freivalds' algorithm","level":5,"score":0.510410487651825},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5017185211181641},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.49557340145111084},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46408650279045105},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.43256378173828125},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4139842092990875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4010123014450073},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3895268142223358},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.19409751892089844},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.09282064437866211},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07023313641548157},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.05872923135757446},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.0},{"id":"https://openalex.org/C173870130","wikidata":"https://www.wikidata.org/wiki/Q8548","display_name":"Dijkstra's algorithm","level":4,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1077464.1077466","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1077464.1077466","pdf_url":null,"source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"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 Algorithms","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":38,"referenced_works":["https://openalex.org/W104109059","https://openalex.org/W152964218","https://openalex.org/W1494735819","https://openalex.org/W1561337879","https://openalex.org/W1823654214","https://openalex.org/W1877375092","https://openalex.org/W1965996575","https://openalex.org/W1967066104","https://openalex.org/W1968408352","https://openalex.org/W1979740015","https://openalex.org/W1981234161","https://openalex.org/W2011182146","https://openalex.org/W2033961328","https://openalex.org/W2035476608","https://openalex.org/W2041094700","https://openalex.org/W2049500052","https://openalex.org/W2058426370","https://openalex.org/W2064909166","https://openalex.org/W2065832012","https://openalex.org/W2069463493","https://openalex.org/W2084375356","https://openalex.org/W2085140829","https://openalex.org/W2089311600","https://openalex.org/W2089437293","https://openalex.org/W2089939118","https://openalex.org/W2093825995","https://openalex.org/W2097747425","https://openalex.org/W2103961582","https://openalex.org/W2148411689","https://openalex.org/W2296148711","https://openalex.org/W2561675875","https://openalex.org/W2610479830","https://openalex.org/W3004540582","https://openalex.org/W3099443264","https://openalex.org/W3145128584","https://openalex.org/W4238323774","https://openalex.org/W4285719527","https://openalex.org/W6606114840"],"related_works":["https://openalex.org/W2919712124","https://openalex.org/W3217647593","https://openalex.org/W3204033665","https://openalex.org/W2108827729","https://openalex.org/W4301181185","https://openalex.org/W2043670592","https://openalex.org/W55853783","https://openalex.org/W3142273471","https://openalex.org/W1521877013","https://openalex.org/W2992231035"],"abstract_inverted_index":{"Let":[0],"A":[1,33],"and":[2,34,54,148],"B":[3,35],"two":[4,166],"n":[5,7,41,44,84,97,105,128],"\u00d7":[6],"matrices":[8,123],"over":[9,56],"a":[10,28,139,144],"ring":[11],"R":[12,57],"(e.g.,":[13],"the":[14,17,65,78,87,108,115,161,170],"reals":[15],"or":[16],"integers)":[18],"each":[19],"containing":[20],"at":[21,184],"most":[22],"m":[23,39,82,103],"nonzero":[24],"elements.":[25],"We":[26,155],"present":[27],"new":[29,88,109,134],"algorithm":[30,89,110,120,135],"that":[31],"multiplies":[32],"using":[36,138],"O":[37,126],"(":[38,127],"0.7":[40],"1.2":[42],"+":[43],"2+":[45,98],"o":[46,99],"(1)":[47,100],")":[48,74,130],"algebraic":[49,131],"operations":[50,75],"(i.e.,":[51],"multiplications,":[52],"additions":[53],"subtractions)":[55],".":[58],"The":[59,133],"na\u00efve":[60],"matrix":[61,118,152,174],"multiplication":[62,119,153,162,175],"algorithm,":[63],"on":[64],"other":[66],"hand,":[67],"may":[68],"need":[69],"to":[70,76],"perform":[71],"\u2126(":[72],"mn":[73],"accomplish":[77],"same":[79],"task.":[80],"For":[81,102],"\u2264":[83,104],"1.14":[85],",":[86,107],"performs":[90],"an":[91],"almost":[92],"optimal":[93],"number":[94],"of":[95,143,163,190],"only":[96,189],"operations.":[101,132],"1.68":[106],"is":[111,136,188],"also":[112,156],"faster":[113],"than":[114,165],"best":[116],"known":[117,171],"for":[121,160,186],"dense":[122],"which":[124],"uses":[125],"2.38":[129],"obtained":[137],"surprisingly":[140],"straightforward":[141],"combination":[142],"simple":[145],"combinatorial":[146],"idea":[147],"existing":[149],"fast":[150,172],"rectangular":[151,173],"algorithms.":[154],"obtain":[157],"improved":[158],"algorithms":[159,176],"more":[164],"sparse":[167],"matrices.":[168],"As":[169],"are":[177],"far":[178],"from":[179],"being":[180],"practical,":[181],"our":[182],"result,":[183],"least":[185],"now,":[187],"theoretical":[191],"value.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":21},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":20},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":18}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}