{"id":"https://openalex.org/W2524409436","doi":"https://doi.org/10.1007/s00037-018-0172-8","title":"Asymptotic tensor rank of graph tensors: beyond matrix multiplication","display_name":"Asymptotic tensor rank of graph tensors: beyond matrix multiplication","publication_year":2018,"publication_date":"2018-09-29","ids":{"openalex":"https://openalex.org/W2524409436","doi":"https://doi.org/10.1007/s00037-018-0172-8","mag":"2524409436"},"language":"en","primary_location":{"id":"doi:10.1007/s00037-018-0172-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-018-0172-8","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1609.07476","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Matthias Christandl","orcid":null},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Matthias Christandl","raw_affiliation_strings":["Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"middle","author":{"id":null,"display_name":"P\u00e9ter Vrana","orcid":null},"institutions":[{"id":"https://openalex.org/I29770179","display_name":"Budapest University of Technology and Economics","ror":"https://ror.org/02w42ss30","country_code":"HU","type":"education","lineage":["https://openalex.org/I29770179"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"P\u00e9ter Vrana","raw_affiliation_strings":["Department of Geometry, Budapest University of Technology and Economics, Egry J\u00f3zsef u. 1., 1111, Budapest, Hungary"],"affiliations":[{"raw_affiliation_string":"Department of Geometry, Budapest University of Technology and Economics, Egry J\u00f3zsef u. 1., 1111, Budapest, Hungary","institution_ids":["https://openalex.org/I29770179"]}]},{"author_position":"last","author":{"id":null,"display_name":"Jeroen Zuiddam","orcid":null},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Jeroen Zuiddam","raw_affiliation_strings":["Centrum Wiskunde & Informatica Science Park 123, 1098 XG, Amsterdam, Netherlands"],"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde & Informatica Science Park 123, 1098 XG, Amsterdam, Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I124055696"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.5031,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.53342428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"28","issue":"1","first_page":"57","last_page":"111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.8047000169754028,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.8047000169754028,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.11159999668598175,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.012900000438094139,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/strassen-algorithm","display_name":"Strassen algorithm","score":0.9239000082015991},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.8331999778747559},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.659600019454956},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6187999844551086},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5986999869346619},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5629000067710876},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48910000920295715},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.42149999737739563}],"concepts":[{"id":"https://openalex.org/C39096654","wikidata":"https://www.wikidata.org/wiki/Q728507","display_name":"Strassen algorithm","level":4,"score":0.9239000082015991},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.8331999778747559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7904999852180481},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.659600019454956},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6541000008583069},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6187999844551086},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5986999869346619},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5629000067710876},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48910000920295715},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46880000829696655},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.40149998664855957},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.32989999651908875},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.2833999991416931},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.27399998903274536},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.2685000002384186},{"id":"https://openalex.org/C164154869","wikidata":"https://www.wikidata.org/wiki/Q901927","display_name":"Critical exponent","level":3,"score":0.26669999957084656},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.260699987411499}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/s00037-018-0172-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-018-0172-8","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","raw_type":"journal-article"},{"id":"pmh:oai:dare.uva.nl:openaire_cris_publications/8a1e28b4-8863-4c33-8389-d60bc6737670","is_oa":false,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/asymptotic-tensor-rank-of-graph-tensors-beyond-matrix-multiplication(8a1e28b4-8863-4c33-8389-d60bc6737670).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Christandl, M, Vrana, P & Zuiddam, J 2019, 'Asymptotic tensor rank of graph tensors: beyond matrix multiplication', Computational Complexity, vol. 28, no. 1, pp. 57-111. https://doi.org/10.1007/s00037-018-0172-8","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1609.07476","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.07476","pdf_url":"https://arxiv.org/pdf/1609.07476","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"},{"id":"pmh:oai:cwi.nl:26707","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/26707","pdf_url":"https://arxiv.org/pdf/1609.07476","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"info:eu-repo/semantics/other"},{"id":"pmh:cwi:oai:cwi.nl:28609","is_oa":false,"landing_page_url":"https://ir.cwi.nl/pub/28609","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational Complexity, 28(1), 57 - 111","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/c8656270-a072-4edc-bd44-fee2264edc84","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85063048708&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Christandl , M , Vrana , P & Zuiddam , J 2019 , ' Asymptotic tensor rank of graph tensors : beyond matrix multiplication ' , Computational Complexity , vol. 28 , no. 1 , pp. 57-111 . https://doi.org/10.1007/s00037-018-0172-8","raw_type":"article"},{"id":"pmh:uvapub:oai:dare.uva.nl:publications/8a1e28b4-8863-4c33-8389-d60bc6737670","is_oa":false,"landing_page_url":"https://dare.uva.nl/personal/pure/en/publications/asymptotic-tensor-rank-of-graph-tensors-beyond-matrix-multiplication(8a1e28b4-8863-4c33-8389-d60bc6737670).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational Complexity, 28(1), 57 - 111. Birkhauser Verlag Basel","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1609.07476","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.07476","pdf_url":"https://arxiv.org/pdf/1609.07476","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W135913015","https://openalex.org/W403233219","https://openalex.org/W1974928788","https://openalex.org/W1977699786","https://openalex.org/W1978102058","https://openalex.org/W1979740015","https://openalex.org/W2015819231","https://openalex.org/W2017154611","https://openalex.org/W2023724794","https://openalex.org/W2035476608","https://openalex.org/W2058790613","https://openalex.org/W2114177725","https://openalex.org/W2120248756","https://openalex.org/W2169638123","https://openalex.org/W2169968099","https://openalex.org/W2294242001","https://openalex.org/W2297982685","https://openalex.org/W2435088519","https://openalex.org/W4231247888"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2016-10-07T00:00:00"}