{"id":"https://openalex.org/W2765635219","doi":"https://doi.org/10.1109/hpec.2017.8091046","title":"First look: Linear algebra-based triangle counting without matrix multiplication","display_name":"First look: Linear algebra-based triangle counting without matrix multiplication","publication_year":2017,"publication_date":"2017-09-01","ids":{"openalex":"https://openalex.org/W2765635219","doi":"https://doi.org/10.1109/hpec.2017.8091046","mag":"2765635219"},"language":"en","primary_location":{"id":"doi:10.1109/hpec.2017.8091046","is_oa":false,"landing_page_url":"https://doi.org/10.1109/hpec.2017.8091046","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE High Performance Extreme Computing Conference (HPEC)","raw_type":"proceedings-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/A5019607600","display_name":"Tze Meng Low","orcid":"https://orcid.org/0000-0002-5179-8249"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tze Meng Low","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070972086","display_name":"Varun Nagaraj Rao","orcid":"https://orcid.org/0000-0002-4692-2196"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Varun Nagaraj Rao","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100376654","display_name":"Matthew Lee","orcid":"https://orcid.org/0000-0001-8190-608X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew Lee","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019066795","display_name":"Doru Thom Popovici","orcid":"https://orcid.org/0000-0002-7271-8092"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Doru Popovici","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062806943","display_name":"Franz Franchetti","orcid":"https://orcid.org/0000-0002-3529-8973"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Franz Franchetti","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028007059","display_name":"Scott McMillan","orcid":"https://orcid.org/0000-0003-1868-5178"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]},{"id":"https://openalex.org/I114772536","display_name":"Software Engineering Institute","ror":"https://ror.org/01xqjjn94","country_code":"US","type":"facility","lineage":["https://openalex.org/I114772536","https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Scott McMillan","raw_affiliation_strings":["Software Engineering Institute, Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Software Engineering Institute, Carnegie Mellon University","institution_ids":["https://openalex.org/I114772536","https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5019607600"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":2.2191,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.8940868,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"6"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9850999712944031,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9811000227928162,"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/linear-algebra","display_name":"Linear algebra","score":0.6496461033821106},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"Matrix algebra","score":0.6341084241867065},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.5902481079101562},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5691556334495544},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4939313530921936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47227180004119873},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43636542558670044},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.42358145117759705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3751601576805115},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30544114112854004},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2215016484260559},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10193568468093872},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07730451226234436},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.0657849907875061}],"concepts":[{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.6496461033821106},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.6341084241867065},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.5902481079101562},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5691556334495544},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4939313530921936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47227180004119873},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43636542558670044},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.42358145117759705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3751601576805115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30544114112854004},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2215016484260559},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10193568468093872},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07730451226234436},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0657849907875061},{"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/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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/hpec.2017.8091046","is_oa":false,"landing_page_url":"https://doi.org/10.1109/hpec.2017.8091046","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE High Performance Extreme Computing Conference (HPEC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1665157575","https://openalex.org/W1991858502","https://openalex.org/W2016311778","https://openalex.org/W2060064441","https://openalex.org/W2518858713","https://openalex.org/W2747404479","https://openalex.org/W2755088640","https://openalex.org/W3100734586","https://openalex.org/W6726122863"],"related_works":["https://openalex.org/W3099313426","https://openalex.org/W4287593139","https://openalex.org/W2036954759","https://openalex.org/W2057797376","https://openalex.org/W2090319426","https://openalex.org/W752783541","https://openalex.org/W2506252583","https://openalex.org/W1506547947","https://openalex.org/W2048249848","https://openalex.org/W4206336957"],"abstract_inverted_index":{"Linear":[0],"algebra-based":[1],"approaches":[2,18,42],"to":[3,19,98],"exact":[4],"triangle":[5,63,75],"counting":[6,64],"often":[7,23],"require":[8],"sparse":[9,87],"matrix":[10,28,67,88,107],"multiplication":[11],"as":[12],"a":[13,47,69],"primitive":[14],"operation.":[15],"Non-linear":[16],"algebra":[17],"the":[20,26,30,52,56,62,85,93,99,105,109,134,141],"same":[21,94],"problem":[22],"assume":[24],"that":[25,40,50,72,92,104,116,123,140],"adjacency":[27,106],"of":[29,108],"graph":[31,110],"is":[32,96,111,124],"not":[33,60,112],"available.":[34,113],"In":[35,81],"this":[36],"paper,":[37],"we":[38,90],"show":[39,91,115,139],"both":[41],"can":[43,78,144],"be":[44,79,145],"unified":[45],"into":[46,66],"single":[48],"approach":[49,118],"separates":[51],"data":[53],"format":[54],"from":[55],"algorithm":[57,65,71,95,101],"design.":[58],"By":[59],"casting":[61],"multiplication,":[68],"different":[70],"counts":[73],"each":[74],"exactly":[76],"once":[77],"identified.":[80],"addition,":[82],"by":[83],"choosing":[84],"appropriate":[86],"format,":[89],"equivalent":[97],"compact-forward":[100],"attained":[102],"assuming":[103],"We":[114,137],"our":[117],"yields":[119],"an":[120],"initial":[121,142],"implementation":[122,143],"between":[125],"69":[126],"and":[127],"more":[128],"than":[129,133],"2000":[130],"times":[131],"faster":[132],"reference":[135],"implementation.":[136],"also":[138],"easily":[146],"parallelized":[147],"on":[148],"shared":[149],"memory":[150],"systems.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
