{"id":"https://openalex.org/W1985926973","doi":"https://doi.org/10.1002/(sici)1096-9128(199705)9:5<345::aid-cpe258>3.0.co;2-7","title":"A poly-algorithm for parallel dense matrix multiplication on two-dimensional process grid topologies","display_name":"A poly-algorithm for parallel dense matrix multiplication on two-dimensional process grid topologies","publication_year":1997,"publication_date":"1997-05-01","ids":{"openalex":"https://openalex.org/W1985926973","doi":"https://doi.org/10.1002/(sici)1096-9128(199705)9:5<345::aid-cpe258>3.0.co;2-7","mag":"1985926973"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1096-9128(199705)9:5<345::aid-cpe258>3.0.co;2-7","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-9128(199705)9:5<345::aid-cpe258>3.0.co;2-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210209928","display_name":"Concurrency Practice and Experience","issn_l":"1040-3108","issn":["1040-3108","1096-9128"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Concurrency: Practice and Experience","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/A5110561344","display_name":"Jiaying Li","orcid":null},"institutions":[{"id":"https://openalex.org/I99041443","display_name":"Mississippi State University","ror":"https://ror.org/0432jq872","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I99041443"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Li","raw_affiliation_strings":["Department of Computer Science & NSF Engineering Research Center, Mississippi State University, Mississippi State, MS 39762, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science & NSF Engineering Research Center, Mississippi State University, Mississippi State, MS 39762, USA","institution_ids":["https://openalex.org/I99041443"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026440046","display_name":"Anthony Skjellum","orcid":"https://orcid.org/0000-0001-5252-6600"},"institutions":[{"id":"https://openalex.org/I99041443","display_name":"Mississippi State University","ror":"https://ror.org/0432jq872","country_code":"US","type":"education","lineage":["https://openalex.org/I4210141039","https://openalex.org/I99041443"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Skjellum","raw_affiliation_strings":["Department of Computer Science & NSF Engineering Research Center, Mississippi State University, Mississippi State, MS 39762, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science & NSF Engineering Research Center, Mississippi State University, Mississippi State, MS 39762, USA","institution_ids":["https://openalex.org/I99041443"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057085539","display_name":"Robert D. Falgout","orcid":"https://orcid.org/0000-0003-4884-0087"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. D. Falgout","raw_affiliation_strings":["Center for Computational Sciences and Engineering, L-316, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational Sciences and Engineering, L-316, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA","institution_ids":["https://openalex.org/I1282311441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026440046"],"corresponding_institution_ids":["https://openalex.org/I99041443"],"apc_list":null,"apc_paid":null,"fwci":1.0385,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.80403868,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"9","issue":"5","first_page":"345","last_page":"389"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9986000061035156,"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/T10715","display_name":"Distributed and Parallel Computing Systems","score":0.9986000061035156,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9983000159263611,"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":0.9961000084877014,"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/correctness","display_name":"Correctness","score":0.7804999351501465},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7210732698440552},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.6787242889404297},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6587912440299988},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5400468111038208},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.4674542546272278},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3237507939338684},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2401132881641388}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.7804999351501465},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7210732698440552},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6787242889404297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6587912440299988},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5400468111038208},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.4674542546272278},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3237507939338684},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2401132881641388},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/(sici)1096-9128(199705)9:5<345::aid-cpe258>3.0.co;2-7","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1096-9128(199705)9:5<345::aid-cpe258>3.0.co;2-7","pdf_url":null,"source":{"id":"https://openalex.org/S4210209928","display_name":"Concurrency Practice and Experience","issn_l":"1040-3108","issn":["1040-3108","1096-9128"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Concurrency: Practice and Experience","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.51.6918","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.6918","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.msstate.edu/staff/tony/public_html/documents/Toolbox/poly95.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.56.7808","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.7808","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://www.cs.msstate.edu/publications/theses_dissertations/li96.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1559533846","https://openalex.org/W1868410565","https://openalex.org/W1984032202","https://openalex.org/W2029342163","https://openalex.org/W2035476608","https://openalex.org/W2099679697","https://openalex.org/W2120490947"],"related_works":["https://openalex.org/W2404647514","https://openalex.org/W4247536566","https://openalex.org/W1667647204","https://openalex.org/W2018477250","https://openalex.org/W3119814709","https://openalex.org/W4241418540","https://openalex.org/W1508895727","https://openalex.org/W2725786787","https://openalex.org/W4283160672","https://openalex.org/W1604988569"],"abstract_inverted_index":{"In":[0],"this":[1,60,151],"paper,":[2],"we":[3,55],"present":[4],"several":[5],"new":[6,210],"and":[7,53,76,103,109,113,143,168,209],"generalized":[8],"parallel":[9],"dense":[10],"matrix":[11,99,142,165,178],"multiplication":[12,166,179],"algorithms":[13,29,42,67,167,180,211],"of":[14,62,97,161,163,206],"the":[15,49,71,95,98,105,137,159,174,185,203,207],"form":[16],"C":[17,22],"=":[18],"\u03b1AB":[19],"+":[20],"\u03b2":[21],"on":[23,36,140,184],"two-dimensional":[24],"process":[25],"grid":[26,144],"topologies.":[27],"These":[28],"can":[30],"deal":[31],"with":[32],"rectangular":[33,37],"matrices":[34],"distributed":[35],"grids.":[38],"We":[39,101,116,129,157],"classify":[40],"these":[41,66,164,177],"coherently":[43],"into":[44],"three":[45],"categories":[46],"according":[47],"to":[48,149,154,196],"communication":[50],"primitives":[51],"used":[52],"thus":[54,77],"offer":[56],"a":[57,81,119],"taxonomy":[58,208],"for":[59,85,172],"family":[61],"related":[63],"algorithms.":[64],"All":[65,176],"are":[68,192],"represented":[69],"in":[70,194],"data":[72,83,106,122,127],"distribution":[73,84,107,123],"independent":[74],"approach":[75,148],"do":[78],"not":[79],"require":[80],"specific":[82],"correctness.":[86],"The":[87,189],"algorithmic":[88,114],"compatibility":[89,112],"condition":[90],"result":[91],"shown":[92],"here":[93],"ensures":[94],"correctness":[96],"multiplication.":[100],"define":[102],"extend":[104],"functions":[108],"introduce":[110],"permutation":[111,120],"compatibility.":[115],"also":[117],"discuss":[118],"compatible":[121],"(modified":[124],"virtual":[125],"2D":[126],"distribution).":[128],"conclude":[130],"that":[131],"no":[132],"single":[133],"algorithm":[134],"always":[135],"achieves":[136],"best":[138],"performance":[139,200],"different":[141],"shapes.":[145],"A":[146],"practical":[147],"resolve":[150],"dilemma":[152],"is":[153],"use":[155],"poly-algorithms.":[156],"analyze":[158],"characteristics":[160],"each":[162],"provide":[169],"initial":[170],"heuristics":[171],"using":[173],"poly-algorithm.":[175],"have":[181],"been":[182],"tested":[183],"IBM":[186],"SP2":[187],"system.":[188],"experimental":[190],"results":[191],"presented":[193],"order":[195],"demonstrate":[197],"their":[198],"relative":[199],"characteristics,":[201],"motivating":[202],"combined":[204],"value":[205],"introduced":[212],"here.":[213],"\u00a9":[214],"1997":[215],"by":[216],"John":[217],"Wiley":[218],"&":[219],"Sons,":[220],"Ltd.":[221]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
