{"id":"https://openalex.org/W2136589970","doi":"https://doi.org/10.1145/2591796.2591824","title":"Lower bounds for depth 4 formulas computing iterated matrix multiplication","display_name":"Lower bounds for depth 4 formulas computing iterated matrix multiplication","publication_year":2014,"publication_date":"2014-05-31","ids":{"openalex":"https://openalex.org/W2136589970","doi":"https://doi.org/10.1145/2591796.2591824","mag":"2136589970"},"language":"en","primary_location":{"id":"doi:10.1145/2591796.2591824","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2591796.2591824","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5004130370","display_name":"Herv\u00e9 Fournier","orcid":null},"institutions":[{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Herv\u00e9 Fournier","raw_affiliation_strings":["Institut de Math\u00e9matiques de Jussieu, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu, Paris, France","institution_ids":["https://openalex.org/I3017942884"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083072245","display_name":"Nutan Limaye","orcid":"https://orcid.org/0000-0002-0238-1674"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Nutan Limaye","raw_affiliation_strings":["Indian Institute of Technology, Bombay, Mumbai, India","Indian Institute of Technology-Bombay, Mumbai, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology, Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology-Bombay, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072821588","display_name":"Guillaume Malod","orcid":"https://orcid.org/0000-0003-2105-9979"},"institutions":[{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Guillaume Malod","raw_affiliation_strings":["Institut de Math\u00e9matiques de Jussieu, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu, Paris, France","institution_ids":["https://openalex.org/I3017942884"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025305994","display_name":"Srikanth Srinivasan","orcid":"https://orcid.org/0000-0001-6491-124X"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Srikanth Srinivasan","raw_affiliation_strings":["Indian Institute of Technology, Bombay, Mumbai, India","Indian Institute of Technology-Bombay, Mumbai, India#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology, Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Indian Institute of Technology-Bombay, Mumbai, India#TAB#","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.4298,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.99292035,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"128","last_page":"135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9994999766349792,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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/matrix-multiplication","display_name":"Matrix multiplication","score":0.854001522064209},{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.7972147464752197},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7924212217330933},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6749376058578491},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6636965870857239},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5806272625923157},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5349430441856384},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5211158394813538},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4517192840576172},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.444479763507843},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.44065943360328674},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3331156373023987},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21684443950653076},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20884153246879578},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17479398846626282},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06019073724746704}],"concepts":[{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.854001522064209},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.7972147464752197},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7924212217330933},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6749376058578491},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6636965870857239},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5806272625923157},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5349430441856384},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5211158394813538},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4517192840576172},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.444479763507843},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.44065943360328674},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3331156373023987},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21684443950653076},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20884153246879578},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17479398846626282},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06019073724746704},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"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:10.1145/2591796.2591824","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2591796.2591824","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-sixth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321027","display_name":"Indo-French Centre for the Promotion of Advanced Research","ror":"https://ror.org/017aem598"},{"id":"https://openalex.org/F4320323399","display_name":"Universit\u00e9 Paris Diderot","ror":"https://ror.org/02n7qrg46"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W64656188","https://openalex.org/W1508771701","https://openalex.org/W1554948556","https://openalex.org/W1582514549","https://openalex.org/W1878491781","https://openalex.org/W1964748897","https://openalex.org/W1988938797","https://openalex.org/W1989274820","https://openalex.org/W1994433543","https://openalex.org/W2016576580","https://openalex.org/W2017290750","https://openalex.org/W2023541349","https://openalex.org/W2026944800","https://openalex.org/W2056881179","https://openalex.org/W2060270693","https://openalex.org/W2069546133","https://openalex.org/W2071105597","https://openalex.org/W2087664562","https://openalex.org/W2110206454","https://openalex.org/W2128510017","https://openalex.org/W2170831059","https://openalex.org/W2171403864","https://openalex.org/W2172394696","https://openalex.org/W2179427905","https://openalex.org/W2405068759","https://openalex.org/W2407086813","https://openalex.org/W2408671604","https://openalex.org/W2596694411","https://openalex.org/W2895239415","https://openalex.org/W2952518935","https://openalex.org/W2953277489","https://openalex.org/W2964011532"],"related_works":["https://openalex.org/W2088588293","https://openalex.org/W3209958448","https://openalex.org/W2330467238","https://openalex.org/W4318719034","https://openalex.org/W1979044519","https://openalex.org/W2021611895","https://openalex.org/W2028706721","https://openalex.org/W3144129416","https://openalex.org/W2096585720","https://openalex.org/W3099313426"],"abstract_inverted_index":{"We":[0,9],"study":[1],"the":[2,20,43],"arithmetic":[3,17],"complexity":[4],"of":[5,22,26,45],"iterated":[6],"matrix":[7],"multiplication.":[8],"show":[10],"that":[11],"any":[12],"multilinear":[13],"homogeneous":[14],"depth":[15,53],"4":[16,54],"formula":[18],"computing":[19],"product":[21],"d":[23,38],"generic":[24],"matrices":[25],"size":[27,33],"n":[28],"\u00d7":[29],"n,":[30],"IMMn,d,":[31],"has":[32],"n\u03a9(\u221ad)":[34],"as":[35,37],"long":[36],"=":[39],"nO(1).":[40],"This":[41],"improves":[42],"result":[44],"Nisan":[46],"and":[47],"Wigderson":[48],"(Computational":[49],"Complexity,":[50],"1997)":[51],"for":[52],"set-multilinear":[55],"formulas.":[56]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
