{"id":"https://openalex.org/W3205617095","doi":"https://doi.org/10.1145/3638349","title":"Faster Modular Composition","display_name":"Faster Modular Composition","publication_year":2023,"publication_date":"2023-12-25","ids":{"openalex":"https://openalex.org/W3205617095","doi":"https://doi.org/10.1145/3638349","mag":"3205617095"},"language":"en","primary_location":{"id":"doi:10.1145/3638349","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3638349","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"Journal of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2110.08354","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016685971","display_name":"Vincent Neiger","orcid":"https://orcid.org/0000-0002-8311-9490"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210159265","display_name":"CS Communication & Syst\u00e8mes (France)","ror":"https://ror.org/053hexc75","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210159265"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Vincent Neiger","raw_affiliation_strings":["Sorbonne Universit\u00e9, Paris, France","PolSys - Polynomial Systems (France)"],"raw_orcid":"https://orcid.org/0000-0002-8311-9490","affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9, Paris, France","institution_ids":["https://openalex.org/I39804081"]},{"raw_affiliation_string":"PolSys - Polynomial Systems (France)","institution_ids":["https://openalex.org/I4210159265"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047966261","display_name":"Bruno Salvy","orcid":"https://orcid.org/0000-0002-4313-0679"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bruno Salvy","raw_affiliation_strings":["Inria, Lyon, France"],"raw_orcid":"https://orcid.org/0000-0002-4313-0679","affiliations":[{"raw_affiliation_string":"Inria, Lyon, France","institution_ids":["https://openalex.org/I1326498283"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041679295","display_name":"\u00c9ric Schost","orcid":"https://orcid.org/0000-0002-8638-9357"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"\u00c9ric Schost","raw_affiliation_strings":["University of Waterloo, Waterloo, Canada","CS - Cheriton School of Computer Science [Waterloo] (200 University Avenue West Waterloo, ON, N2L 3G1 - Canada)","University of Waterloo [Waterloo] (200 University Avenue West, Waterloo, ON, Canada N2L 3G1 - Canada)"],"raw_orcid":"https://orcid.org/0000-0002-8638-9357","affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"CS - Cheriton School of Computer Science [Waterloo] (200 University Avenue West Waterloo, ON, N2L 3G1 - Canada)","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"University of Waterloo [Waterloo] (200 University Avenue West, Waterloo, ON, Canada N2L 3G1 - Canada)","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021399584","display_name":"Gilles Villard","orcid":"https://orcid.org/0000-0003-1936-7155"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gilles Villard","raw_affiliation_strings":["CNRS, Lyon, France"],"raw_orcid":"https://orcid.org/0000-0003-1936-7155","affiliations":[{"raw_affiliation_string":"CNRS, Lyon, France","institution_ids":["https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4187,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.85682948,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"71","issue":"2","first_page":"1","last_page":"79"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/composition","display_name":"Composition (language)","score":0.7007756233215332},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.5985177755355835},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35955607891082764},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.14719733595848083},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.10690844058990479},{"id":"https://openalex.org/keywords/literature","display_name":"Literature","score":0.04306316375732422}],"concepts":[{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.7007756233215332},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5985177755355835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35955607891082764},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.14719733595848083},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.10690844058990479},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.04306316375732422}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3638349","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3638349","pdf_url":null,"source":{"id":"https://openalex.org/S118992489","display_name":"Journal of the ACM","issn_l":"0004-5411","issn":["0004-5411","1557-735X"],"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":"Journal of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2110.08354","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.08354","pdf_url":"https://arxiv.org/pdf/2110.08354","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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03380258v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03380258","pdf_url":"https://hal.science/hal-03380258/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of the ACM (JACM), 2024, 71 (2), pp.1-79. ⟨10.1145/3638349⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-03380258v2","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-03380258","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://hal.archives-ouvertes.fr/hal-03380258","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2110.08354","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.08354","pdf_url":"https://arxiv.org/pdf/2110.08354","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":83,"referenced_works":["https://openalex.org/W174479171","https://openalex.org/W208025404","https://openalex.org/W430666788","https://openalex.org/W1502124338","https://openalex.org/W1553454551","https://openalex.org/W1561337879","https://openalex.org/W1564956404","https://openalex.org/W1625225258","https://openalex.org/W1969237032","https://openalex.org/W1979366382","https://openalex.org/W1985813832","https://openalex.org/W1986421748","https://openalex.org/W1986905837","https://openalex.org/W1993840452","https://openalex.org/W1994173643","https://openalex.org/W1994728957","https://openalex.org/W1998322533","https://openalex.org/W2000520486","https://openalex.org/W2000760108","https://openalex.org/W2001224529","https://openalex.org/W2007659444","https://openalex.org/W2010027455","https://openalex.org/W2018818965","https://openalex.org/W2018946319","https://openalex.org/W2019755630","https://openalex.org/W2028552691","https://openalex.org/W2029631600","https://openalex.org/W2030141403","https://openalex.org/W2033961328","https://openalex.org/W2051154648","https://openalex.org/W2052024558","https://openalex.org/W2055223395","https://openalex.org/W2055580199","https://openalex.org/W2057341276","https://openalex.org/W2059887287","https://openalex.org/W2060801388","https://openalex.org/W2071483197","https://openalex.org/W2071558779","https://openalex.org/W2073842331","https://openalex.org/W2080423878","https://openalex.org/W2088713140","https://openalex.org/W2096280747","https://openalex.org/W2100300741","https://openalex.org/W2120248756","https://openalex.org/W2127412655","https://openalex.org/W2145256573","https://openalex.org/W2153077274","https://openalex.org/W2161330625","https://openalex.org/W2168527104","https://openalex.org/W2207819601","https://openalex.org/W2557819255","https://openalex.org/W2603513289","https://openalex.org/W2738987789","https://openalex.org/W2743246826","https://openalex.org/W2785230309","https://openalex.org/W2798813531","https://openalex.org/W2800644154","https://openalex.org/W2809375912","https://openalex.org/W2909065051","https://openalex.org/W2963129602","https://openalex.org/W2963460959","https://openalex.org/W2963464974","https://openalex.org/W2963733895","https://openalex.org/W2969268864","https://openalex.org/W3005706995","https://openalex.org/W3013020064","https://openalex.org/W3046897419","https://openalex.org/W3101040267","https://openalex.org/W3105773606","https://openalex.org/W3116253690","https://openalex.org/W3127569742","https://openalex.org/W3128262951","https://openalex.org/W3134870882","https://openalex.org/W3211991322","https://openalex.org/W4205630623","https://openalex.org/W4213231302","https://openalex.org/W4253468834","https://openalex.org/W4299291835","https://openalex.org/W4313227220","https://openalex.org/W4384389883","https://openalex.org/W4388055159","https://openalex.org/W4390098349","https://openalex.org/W4390575692"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052","https://openalex.org/W2382290278","https://openalex.org/W4395014643"],"abstract_inverted_index":{"A":[0],"new":[1,104],"Las":[2],"Vegas":[3],"algorithm":[4,33,105],"is":[5,101,137,143],"presented":[6],"for":[7,50],"the":[8,22,32,44,48,51,84,103,128],"composition":[9],"of":[10,24,87,93,130,133,139],"two":[11],"polynomials":[12,26],"modulo":[13],"a":[14,91,131],"third":[15],"one,":[16],"over":[17,90],"an":[18],"arbitrary":[19,147],"field.":[20],"When":[21],"degrees":[23],"these":[25],"are":[27],"bounded":[28],"by":[29],"n":[30,37,69,77,108,120],",":[31],"uses":[34],"O":[35,67,118],"(":[36,68,119],"1.43":[38],")":[39,71,122],"field":[40,72,81,92],"operations,":[41,112],"breaking":[42],"through":[43],"3/2":[45],"barrier":[46],"in":[47,64,74,83,107,117],"exponent":[49],"first":[52],"time.":[53],"The":[54],"previous":[55,114],"fastest":[56],"algebraic":[57,134],"algorithms,":[58],"due":[59],"to":[60,145,149],"Brent":[61],"and":[62,76],"Kung":[63],"1978,":[65],"require":[66],"1.63":[70],"operations":[73,82],"general,":[75],"3/2+":[78],"o":[79,110],"(1)":[80,111],"special":[85],"case":[86],"power":[88],"series":[89],"large":[94],"enough":[95],"characteristic.":[96],"If":[97],"cubic-time":[98],"matrix":[99,132],"multiplication":[100],"used,":[102],"runs":[106],"5/3+":[109],"while":[113],"ones":[115],"run":[116],"2":[121],"operations.":[123],"Our":[124],"approach":[125],"relies":[126],"on":[127],"computation":[129],"relations":[135],"that":[136],"typically":[138],"small":[140],"size.":[141],"Randomization":[142],"used":[144],"reduce":[146],"input":[148],"this":[150],"favorable":[151],"situation.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}