{"id":"https://openalex.org/W4381328613","doi":"https://doi.org/10.1145/3589266","title":"Efficient and Portable Einstein Summation in SQL","display_name":"Efficient and Portable Einstein Summation in SQL","publication_year":2023,"publication_date":"2023-06-13","ids":{"openalex":"https://openalex.org/W4381328613","doi":"https://doi.org/10.1145/3589266"},"language":"en","primary_location":{"id":"doi:10.1145/3589266","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3589266","pdf_url":null,"source":{"id":"https://openalex.org/S4387289859","display_name":"Proceedings of the ACM on Management of Data","issn_l":"2836-6573","issn":["2836-6573"],"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":"Proceedings of the ACM on Management of Data","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/A5032039652","display_name":"Mark Blacher","orcid":"https://orcid.org/0009-0007-2009-7996"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mark Blacher","raw_affiliation_strings":["Friedrich Schiller University Jena, Jena, Germany"],"raw_orcid":"https://orcid.org/0009-0007-2009-7996","affiliations":[{"raw_affiliation_string":"Friedrich Schiller University Jena, Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003339926","display_name":"Julien Klaus","orcid":"https://orcid.org/0000-0002-1498-2653"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Julien Klaus","raw_affiliation_strings":["Friedrich Schiller University Jena, Jena, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1498-2653","affiliations":[{"raw_affiliation_string":"Friedrich Schiller University Jena, Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077217557","display_name":"Christoph Staudt","orcid":"https://orcid.org/0009-0000-4250-546X"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph Staudt","raw_affiliation_strings":["Friedrich Schiller University Jena, Jena, Germany"],"raw_orcid":"https://orcid.org/0009-0000-4250-546X","affiliations":[{"raw_affiliation_string":"Friedrich Schiller University Jena, Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091320755","display_name":"S\u00f6ren Laue","orcid":null},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S\u00f6ren Laue","raw_affiliation_strings":["University of Hamburg, Hamburg, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4351-9868","affiliations":[{"raw_affiliation_string":"University of Hamburg, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046213289","display_name":"Viktor Leis","orcid":"https://orcid.org/0000-0001-5676-8017"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Viktor Leis","raw_affiliation_strings":["Technical University of Munich, Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5676-8017","affiliations":[{"raw_affiliation_string":"Technical University of Munich, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027313464","display_name":"Joachim Giesen","orcid":"https://orcid.org/0000-0001-6598-6833"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Joachim Giesen","raw_affiliation_strings":["Friedrich Schiller University Jena, Jena, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6598-6833","affiliations":[{"raw_affiliation_string":"Friedrich Schiller University Jena, Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7109,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.94000647,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"1","issue":"2","first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9991999864578247,"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":0.9991999864578247,"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/T10317","display_name":"Advanced Database Systems and Queries","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/T12292","display_name":"Graph Theory and Algorithms","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/einstein","display_name":"Einstein","score":0.6579549312591553},{"id":"https://openalex.org/keywords/sql","display_name":"SQL","score":0.6450648903846741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6246940493583679},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.512703537940979},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5107676982879639},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4822562336921692},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.434101402759552},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.321274071931839},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2691280245780945},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1923561692237854},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1367412805557251},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11447808146476746},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09801739454269409}],"concepts":[{"id":"https://openalex.org/C146846114","wikidata":"https://www.wikidata.org/wiki/Q901448","display_name":"Einstein","level":2,"score":0.6579549312591553},{"id":"https://openalex.org/C510870499","wikidata":"https://www.wikidata.org/wiki/Q47607","display_name":"SQL","level":2,"score":0.6450648903846741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6246940493583679},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.512703537940979},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5107676982879639},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4822562336921692},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.434101402759552},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.321274071931839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2691280245780945},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1923561692237854},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1367412805557251},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11447808146476746},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09801739454269409}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3589266","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3589266","pdf_url":null,"source":{"id":"https://openalex.org/S4387289859","display_name":"Proceedings of the ACM on Management of Data","issn_l":"2836-6573","issn":["2836-6573"],"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":"Proceedings of the ACM on Management of Data","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309895","display_name":"Carl-Zeiss-Stiftung","ror":"https://ror.org/03ng4kg22"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W1840046823","https://openalex.org/W1992191167","https://openalex.org/W2036265926","https://openalex.org/W2072969317","https://openalex.org/W2086128349","https://openalex.org/W2099655235","https://openalex.org/W2146635036","https://openalex.org/W2260987415","https://openalex.org/W2527672088","https://openalex.org/W2614179415","https://openalex.org/W2747149925","https://openalex.org/W2747774925","https://openalex.org/W2799457717","https://openalex.org/W2810421208","https://openalex.org/W2898123186","https://openalex.org/W2905031525","https://openalex.org/W2910259907","https://openalex.org/W2918033599","https://openalex.org/W2940725065","https://openalex.org/W2949054050","https://openalex.org/W2950460874","https://openalex.org/W2963741498","https://openalex.org/W2970971581","https://openalex.org/W2971327870","https://openalex.org/W2980017474","https://openalex.org/W2993863944","https://openalex.org/W3008970095","https://openalex.org/W3015253292","https://openalex.org/W3027794400","https://openalex.org/W3080724058","https://openalex.org/W3100408144","https://openalex.org/W3100993774","https://openalex.org/W3101479050","https://openalex.org/W3105359761","https://openalex.org/W3120740533","https://openalex.org/W4200337324","https://openalex.org/W4206973626","https://openalex.org/W4207073217","https://openalex.org/W4244523512","https://openalex.org/W4282596171","https://openalex.org/W4292651864","https://openalex.org/W4295312788","https://openalex.org/W6632489444","https://openalex.org/W6638060716","https://openalex.org/W6651768176","https://openalex.org/W6673290415","https://openalex.org/W6677692869","https://openalex.org/W6729942461","https://openalex.org/W6745009862","https://openalex.org/W6758545380","https://openalex.org/W6762801845","https://openalex.org/W6764391041","https://openalex.org/W6767378834","https://openalex.org/W6773724811","https://openalex.org/W6785237705","https://openalex.org/W6785655149","https://openalex.org/W6791715169","https://openalex.org/W6797430902","https://openalex.org/W6804131460"],"related_works":["https://openalex.org/W2963177394","https://openalex.org/W2024638892","https://openalex.org/W763418848","https://openalex.org/W1595229445","https://openalex.org/W1965815883","https://openalex.org/W149041114","https://openalex.org/W4313359513","https://openalex.org/W322408318","https://openalex.org/W4298135613","https://openalex.org/W1583261078"],"abstract_inverted_index":{"Computational":[0],"problems":[1],"ranging":[2],"from":[3],"artificial":[4],"intelligence":[5],"to":[6,83,91,101],"physics":[7],"require":[8],"efficient":[9,86,154],"computations":[10,157],"of":[11,110,137,170],"large":[12,74,93],"tensor":[13,16,27,75],"expressions.":[14],"These":[15],"expressions":[17,28,76],"can":[18,80],"often":[19],"be":[20,81],"represented":[21],"in":[22,29,77,128,148,158],"Einstein":[23,30,37,45,78,94,111,138,155],"notation.":[24],"To":[25],"evaluate":[26],"notation,":[31],"that":[32,58],"is,":[33],"for":[34,165],"the":[35,108,144,149,166],"actual":[36],"summation,":[38],"usually":[39],"external":[40],"libraries":[41],"are":[42],"used.":[43],"Surprisingly,":[44],"summation":[46,95,112,139,156],"operations":[47],"on":[48,114,143],"tensors":[49],"fit":[50],"well":[51],"with":[52],"fundamental":[53],"SQL":[54,87],"constructs.":[55],"We":[56,106],"show":[57],"by":[59],"applying":[60],"only":[61],"four":[62,115],"mapping":[63],"rules":[64],"and":[65,85,131,168],"a":[66],"simple":[67],"decomposition":[68],"scheme":[69],"using":[70],"common":[71],"table":[72],"expressions,":[73],"notation":[79],"translated":[82],"portable":[84],"code.":[88],"The":[89,135],"ability":[90],"execute":[92],"queries":[96,113],"opens":[97],"up":[98],"new":[99,162],"possibilities":[100],"process":[102],"data":[103],"within":[104],"SQL.":[105],"demonstrate":[107],"power":[109],"use":[116],"cases,":[117],"namely":[118],"querying":[119],"triplestore":[120],"data,":[121],"solving":[122],"Boolean":[123],"satisfiability":[124],"problems,":[125],"performing":[126],"inference":[127],"graphical":[129],"models,":[130],"simulating":[132],"quantum":[133],"circuits.":[134],"performance":[136],"queries,":[140],"however,":[141],"depends":[142],"query":[145,171],"engine":[146],"implemented":[147],"database":[150,159],"system.":[151],"Therefore,":[152],"supporting":[153],"systems":[160],"presents":[161],"research":[163],"challenges":[164],"design":[167],"implementation":[169],"engines.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
