{"id":"https://openalex.org/W4393042598","doi":"https://doi.org/10.1145/3652025","title":"Fast Multivariate Multipoint Evaluation over All Finite Fields","display_name":"Fast Multivariate Multipoint Evaluation over All Finite Fields","publication_year":2024,"publication_date":"2024-03-21","ids":{"openalex":"https://openalex.org/W4393042598","doi":"https://doi.org/10.1145/3652025"},"language":"en","primary_location":{"id":"doi:10.1145/3652025","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3652025","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3652025","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3652025","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072953772","display_name":"Vishwas Bhargava","orcid":"https://orcid.org/0009-0005-7869-377X"},"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":true,"raw_author_name":"Vishwas Bhargava","raw_affiliation_strings":["University of Waterloo, Waterloo, Canada"],"raw_orcid":"https://orcid.org/0009-0005-7869-377X","affiliations":[{"raw_affiliation_string":"University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101653312","display_name":"Sumanta Ghosh","orcid":"https://orcid.org/0009-0003-4892-4210"},"institutions":[{"id":"https://openalex.org/I19149307","display_name":"Chennai Mathematical Institute","ror":"https://ror.org/04zp24820","country_code":"IN","type":"education","lineage":["https://openalex.org/I19149307"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sumanta Ghosh","raw_affiliation_strings":["Chennai Mathematical Institute, Chennai, India"],"raw_orcid":"https://orcid.org/0009-0003-4892-4210","affiliations":[{"raw_affiliation_string":"Chennai Mathematical Institute, Chennai, India","institution_ids":["https://openalex.org/I19149307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004777401","display_name":"Zeyu Guo","orcid":"https://orcid.org/0000-0001-7893-4346"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zeyu Guo","raw_affiliation_strings":["The Ohio State University, Columbus, USA"],"raw_orcid":"https://orcid.org/0000-0001-7893-4346","affiliations":[{"raw_affiliation_string":"The Ohio State University, Columbus, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100713973","display_name":"Mrinal Kumar","orcid":"https://orcid.org/0000-0002-6430-0219"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Mrinal Kumar","raw_affiliation_strings":["Tata Institute of Fundamental Research, Mumbai, India","Tata Institute of Fundamental Research, Mumbai Mumbai, India"],"raw_orcid":"https://orcid.org/0000-0002-6430-0219","affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research, Mumbai, India","institution_ids":["https://openalex.org/I11947397"]},{"raw_affiliation_string":"Tata Institute of Fundamental Research, Mumbai Mumbai, India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047283705","display_name":"Chris Umans","orcid":"https://orcid.org/0000-0002-6390-9401"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chris Umans","raw_affiliation_strings":["California Institute of Technology, Pasadena, USA"],"raw_orcid":"https://orcid.org/0000-0002-6390-9401","affiliations":[{"raw_affiliation_string":"California Institute of Technology, Pasadena, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5072953772"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":0.6798,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61395243,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"71","issue":"3","first_page":"1","last_page":"32"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9986000061035156,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9930999875068665,"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/multivariate-statistics","display_name":"Multivariate statistics","score":0.7381641268730164},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5978881120681763},{"id":"https://openalex.org/keywords/multivariate-analysis","display_name":"Multivariate analysis","score":0.43186354637145996},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3574555814266205},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1407802402973175}],"concepts":[{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.7381641268730164},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5978881120681763},{"id":"https://openalex.org/C38180746","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate analysis","level":2,"score":0.43186354637145996},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3574555814266205},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1407802402973175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3652025","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3652025","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3652025","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"}],"best_oa_location":{"id":"doi:10.1145/3652025","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3652025","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3652025","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4412289256","display_name":null,"funder_award_id":"12-R&D-TFR-5.01-0500","funder_id":"https://openalex.org/F4320320768","funder_display_name":"Department of Atomic Energy, Government of India"},{"id":"https://openalex.org/G904619761","display_name":null,"funder_award_id":"12-R&D-TFR-5.01-0500","funder_id":"https://openalex.org/F4320320768","funder_display_name":"Department of Atomic Energy, Government of India"}],"funders":[{"id":"https://openalex.org/F4320320768","display_name":"Department of Atomic Energy, Government of India","ror":"https://ror.org/02m388s04"},{"id":"https://openalex.org/F4320323448","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393042598.pdf","grobid_xml":"https://content.openalex.org/works/W4393042598.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W64496678","https://openalex.org/W134647183","https://openalex.org/W1491152510","https://openalex.org/W1570807665","https://openalex.org/W1625225258","https://openalex.org/W2010393691","https://openalex.org/W2019755630","https://openalex.org/W2108124616","https://openalex.org/W2207819601","https://openalex.org/W2891175669","https://openalex.org/W2941649468","https://openalex.org/W2942585558","https://openalex.org/W3034461385","https://openalex.org/W3211991322","https://openalex.org/W4205630623","https://openalex.org/W4212992501","https://openalex.org/W4225642243","https://openalex.org/W4252614677","https://openalex.org/W6602605468"],"related_works":["https://openalex.org/W2406638334","https://openalex.org/W40745829","https://openalex.org/W4318262572","https://openalex.org/W1978357124","https://openalex.org/W1578824628","https://openalex.org/W2032728545","https://openalex.org/W1570805059","https://openalex.org/W4250754046","https://openalex.org/W4243682621","https://openalex.org/W2036849593"],"abstract_inverted_index":{"Multivariate":[0],"multipoint":[1,34,199,256,302],"evaluation":[2,19,35,257,303],"is":[3,107,142,259,282,343,361],"the":[4,44,97,102,114,139,161,171,202,240,266,269,279,300,335,338,354],"problem":[5,115,304],"of":[6,46,51,87,104,116,127,163,173,188,204,209,221,231,242,268,290,337,356,359],"evaluating":[7],"a":[8,13,29,185,229,251,275,306],"multivariate":[9,33,198,255,301],"polynomial,":[10],"given":[11],"as":[12,120],"coefficient":[14],"vector,":[15],"simultaneously":[16],"at":[17,59,108,344],"multiple":[18],"points.":[20],"In":[21,153],"this":[22,118,136,154,158,357],"work,":[23,155],"we":[24,156],"show":[25],"that":[26,42,208,220,258,278,334],"there":[27],"exists":[28],"deterministic":[30],"algorithm":[31,182,253,298],"for":[32,71,197,254,320],"over":[36,165,177,305],"any":[37],"finite":[38,167,179,307,339],"field":[39,141,280,308,340],"\\(\\mathbb":[40,309,341],"{F}\\)":[41,310,342],"outputs":[43],"evaluations":[45],"an":[47,121,245,285],"m":[48,106],"-variate":[49],"polynomial":[50],"degree":[52],"less":[53,149],"than":[54,150],"d":[55,289],"in":[56,62,244,263,288,311],"each":[57],"variable":[58],"N":[60],"points":[61],"time,":[63,312],"\\(\\begin{equation*}":[64,313],"(d^m+N)^{1+o(1)}\\cdot":[65,314],"{{\\sf":[66,315],"poly}}(m,d,\\log":[67,316],"|\\mathbb":[68,317],"{F}|),":[69,318],"\\end{equation*}\\)":[70,319],"all":[72,77,166,178,321,326],"\\(m\\in":[73,322],"\\mathbb":[74,81,323,330],"{N}\\)":[75,82,324,331],"and":[76,89,93,111,131,146,175,206,212,216,219,225,233,325],"sufficiently":[78,327],"large":[79,145,328],"\\(d\\in":[80,329],".":[83,152,293],"A":[84,124],"previous":[85],"work":[86,126],"Kedlaya":[88,174,205],"Umans":[90,176],"(FOCS":[91],"2008":[92],"SICOMP":[94],"2011)":[95],"achieved":[96],"same":[98],"time":[99],"complexity":[100],"when":[101,138],"number":[103,162,237],"variables":[105,164],"most":[109,345],"\\(d^{o(1)}\\)":[110,151],"had":[112],"left":[113],"removing":[117],"condition":[119],"open":[122],"problem.":[123],"recent":[125],"Bhargava,":[128,222],"Ghosh,":[129,223],"Kumar,":[130,224],"Mohapatra":[132],"(STOC":[133],"2022)":[134],"answered":[135],"question":[137,172],"underlying":[140],"not":[143],"too":[144],"has":[147],"characteristic":[148],"remove":[157],"constraint":[159],"on":[160,184],"fields,":[168],"thereby":[169],"answering":[170],"fields.":[180],"Our":[181],"relies":[183],"non-trivial":[186],"combination":[187],"ideas":[189],"from":[190,235],"three":[191],"seemingly":[192],"different":[193],"previously":[194],"known":[195],"algorithms":[196,203],"evaluation,":[200],"namely":[201],"Umans,":[207],"Bj\u00f6rklund,":[210],"Kaski,":[211],"Williams":[213],"(IPEC":[214],"2017":[215],"Algorithmica":[217],"2019),":[218],"Mohapatra,":[226],"together":[227],"with":[228],"result":[230],"Bombieri":[232],"Vinogradov":[234],"analytic":[236],"theory":[238],"about":[239],"distribution":[241],"primes":[243],"arithmetic":[246],"progression.":[247],"We":[248],"also":[249],"present":[250],"second":[252,297],"completely":[260],"elementary":[261],"and,":[262],"particular,":[264],"avoids":[265],"use":[267],"Bombieri\u2013Vinogradov":[270],"theorem.":[271],"However,":[272],"it":[273],"requires":[274],"mild":[276],"assumption":[277],"size":[281,336],"bounded":[283,291],"by":[284],"exponential":[286],"tower":[287,358],"height":[292,355],"More":[294],"specifically,":[295],"our":[296],"solves":[299],",":[332,352],"provided":[333],"\\((\\exp":[346],"(\\exp":[347,348,350],"(\\cdots":[349],"(d)))))\\)":[351],"where":[353],"exponentials":[360],"fixed.":[362]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}