{"id":"https://openalex.org/W2158950080","doi":"https://doi.org/10.1145/1940475.1940484","title":"Complexity and performance results for non FFT-based univariate polynomial multiplication","display_name":"Complexity and performance results for non FFT-based univariate polynomial multiplication","publication_year":2011,"publication_date":"2011-01-28","ids":{"openalex":"https://openalex.org/W2158950080","doi":"https://doi.org/10.1145/1940475.1940484","mag":"2158950080"},"language":"en","primary_location":{"id":"doi:10.1145/1940475.1940484","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1940475.1940484","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","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/A5114254228","display_name":"Muhammad F. I. Chowdhury","orcid":null},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Muhammad F.I. Chowdhury","raw_affiliation_strings":["University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081832433","display_name":"Marc Moreno Maza","orcid":"https://orcid.org/0000-0003-3011-0756"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Marc Moreno Maza","raw_affiliation_strings":["University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102914756","display_name":"Wei Pan","orcid":"https://orcid.org/0000-0001-5122-626X"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Wei Pan","raw_affiliation_strings":["University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041679295","display_name":"\u00c9ric Schost","orcid":"https://orcid.org/0000-0002-8638-9357"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"\u00c9ric Schost","raw_affiliation_strings":["University of Western Ontario, London, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"University of Western Ontario, London, Ontario, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5114254228"],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17692131,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"44","issue":"3/4","first_page":"99","last_page":"100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9979000091552734,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9979000091552734,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9955000281333923,"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/univariate","display_name":"Univariate","score":0.8264926671981812},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7068012952804565},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.6759713888168335},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.5554201602935791},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5376718044281006},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4690081775188446},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4104493260383606},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3478877544403076},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30481815338134766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2708930969238281},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.08810627460479736}],"concepts":[{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.8264926671981812},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7068012952804565},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.6759713888168335},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.5554201602935791},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5376718044281006},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4690081775188446},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4104493260383606},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3478877544403076},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30481815338134766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2708930969238281},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.08810627460479736},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1940475.1940484","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1940475.1940484","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2393892148","https://openalex.org/W4280528130","https://openalex.org/W4242837953","https://openalex.org/W2289698831","https://openalex.org/W2555698354","https://openalex.org/W2020253731","https://openalex.org/W1976073875","https://openalex.org/W2085767481","https://openalex.org/W2576749362","https://openalex.org/W2362816532"],"abstract_inverted_index":{"Today's":[0],"parallel":[1,70],"hardware":[2],"architectures":[3],"and":[4,24,56,66],"computer":[5],"memory":[6],"hierarchies":[7],"enforce":[8],"revisiting":[9],"fundamental":[10],"algorithms":[11,40,45],"which":[12],"were":[13],"often":[14],"designed":[15],"with":[16,25],"algebraic":[17],"complexity":[18,22,65],"as":[19,29],"the":[20,30,51,54,57],"main":[21,31],"measure":[23],"sequential":[26],"running":[27],"time":[28],"performance":[32],"counter.":[33],"This":[34],"study":[35],"is":[36],"devoted":[37],"to":[38],"two":[39],"for":[41],"univariate":[42,59],"polynomial":[43],"multiplication":[44],"that":[46],"are":[47,48],"independent":[49],"of":[50],"coefficient":[52],"ring:":[53],"plain":[55],"Toom-Cook":[58],"multiplications.":[60],"We":[61],"analyze":[62],"their":[63,69],"cache":[64],"report":[67],"on":[68],"implementations":[71],"in":[72],"Cilk++.":[73]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}