{"id":"https://openalex.org/W2113291984","doi":"https://doi.org/10.1137/0219073","title":"Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields","display_name":"Fast Parallel Algorithms for Sparse Multivariate Polynomial Interpolation over Finite Fields","publication_year":1990,"publication_date":"1990-12-01","ids":{"openalex":"https://openalex.org/W2113291984","doi":"https://doi.org/10.1137/0219073","mag":"2113291984"},"language":"en","primary_location":{"id":"doi:10.1137/0219073","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0219073","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5103580707","display_name":"Dima Yu. Grigoriev","orcid":null},"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":"Dima Yu. Grigoriev","raw_affiliation_strings":["Centre National De La: Recherche Scientifique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre National De La: Recherche Scientifique","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108090276","display_name":"Marek Karpi\u0144ski","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]},{"id":"https://openalex.org/I2800906181","display_name":"St. Petersburg Department of Steklov Institute of Mathematics","ror":"https://ror.org/030h9s280","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2800906181","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]}],"countries":["DE","RU","US"],"is_corresponding":false,"raw_author_name":"Marek Karpinski","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695. 1059","Department of Computer Science, University of Bonn, 5300 Bonn 1, Federal Republic of Germany","? Steklov Institute of Mathematics, Soviet Academy of Sciences, Leningrad 191011, USSR"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695. 1059","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Department of Computer Science, University of Bonn, 5300 Bonn 1, Federal Republic of Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"? Steklov Institute of Mathematics, Soviet Academy of Sciences, Leningrad 191011, USSR","institution_ids":["https://openalex.org/I2801160905","https://openalex.org/I2800906181"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071271321","display_name":"Michael F. Singer","orcid":"https://orcid.org/0000-0001-6526-8313"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael F. Singer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":28.291,"has_fulltext":false,"cited_by_count":131,"citation_normalized_percentile":{"value":0.99515062,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"19","issue":"6","first_page":"1059","last_page":"1063"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.998199999332428,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.998199999332428,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980999827384949,"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/T10237","display_name":"Cryptography and Data Security","score":0.9979000091552734,"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/finite-field","display_name":"Finite field","score":0.6725984811782837},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6494377255439758},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6392217874526978},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.546669602394104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5322743654251099},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.5254548788070679},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5050581097602844},{"id":"https://openalex.org/keywords/black-box","display_name":"Black box","score":0.4520849287509918},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45032161474227905},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4373665452003479},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4108130931854248},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27154096961021423},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17303121089935303},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.14938443899154663},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09089505672454834}],"concepts":[{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6725984811782837},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6494377255439758},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6392217874526978},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.546669602394104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5322743654251099},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.5254548788070679},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5050581097602844},{"id":"https://openalex.org/C94966114","wikidata":"https://www.wikidata.org/wiki/Q29256","display_name":"Black box","level":2,"score":0.4520849287509918},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45032161474227905},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4373665452003479},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4108130931854248},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27154096961021423},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17303121089935303},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.14938443899154663},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09089505672454834},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0219073","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0219073","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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":14,"referenced_works":["https://openalex.org/W6968995","https://openalex.org/W1517585663","https://openalex.org/W1569612250","https://openalex.org/W1599026900","https://openalex.org/W1606480398","https://openalex.org/W1973452640","https://openalex.org/W1974872521","https://openalex.org/W2017205387","https://openalex.org/W2049161913","https://openalex.org/W2049337025","https://openalex.org/W2057182494","https://openalex.org/W2080132708","https://openalex.org/W4206794571","https://openalex.org/W4256131629"],"related_works":["https://openalex.org/W2047881532","https://openalex.org/W2285795935","https://openalex.org/W4389072557","https://openalex.org/W4319452366","https://openalex.org/W1525419764","https://openalex.org/W2587745679","https://openalex.org/W2607125540","https://openalex.org/W2611087371","https://openalex.org/W2738041067","https://openalex.org/W2347333173"],"abstract_inverted_index":{"The":[0,254],"authors":[1],"consider":[2],"the":[3,20,23,29,36,46,51,54,62,73,90,113,125,154,174,179,195,200,209,212,248,259,281,301],"problem":[4,282],"of":[5,22,28,64,161,173,181,194,202,230,237,251,256,263,279,283,300],"reconstructing":[6],"(i.e.,":[7,304],"interpolating)":[8],"a":[9,14,41,119,234,275,286,297],"t-sparse":[10,103,287],"multivariate":[11],"polynomial":[12,24,37,52,74,94,126,260,288],"given":[13],"black":[15,47,120],"box":[16,48,121],"which":[17],"will":[18],"produce":[19],"value":[21,27],"for":[25,101,159,208,224],"any":[26],"arguments.":[30],"It":[31],"is":[32,61,68,131,226,289,312],"shown":[33],"that,":[34],"if":[35,285],"has":[38],"coefficients":[39],"in":[40,53,75,129,171,192,296,314],"finite":[42,106],"field":[43,55,229,303,311],"$GF[q]$":[44,130],"and":[45,81,108,141,168,189,240,267],"can":[49,244],"evaluate":[50],"$GF[q^{\\ulcorner":[56],"2\\log_{q}(nt)+3":[57],"\\urcorner}]$,":[58],"where":[59],"n":[60],"number":[63],"variables,":[65],"then":[66],"there":[67],"an":[69,305],"algorithm":[70,88,96,217],"to":[71,148,247,291],"interpolate":[72],"$O(\\log^3":[76],"(nt))$":[77],"boolean":[78,99],"parallel":[79],"time":[80,95,211],"$O(n^2":[82],"t^6":[83],"\\log^2":[84],"nt)$":[85],"processors.":[86],"This":[87,150],"yields":[89,207],"first":[91,210],"efficient":[92,116,155],"deterministic":[93,156,214],"(and":[97],"moreover":[98],"$NC$-algorithm)":[100],"interpolating":[102],"polynomials":[104],"over":[105,219,309],"fields":[107,160],"should":[109],"be":[110,245],"contrasted":[111],"with":[112,153,273],"fact":[114],"that":[115,122,227],"interpolation":[117,157],"using":[118],"only":[123],"evaluates":[124],"at":[127],"points":[128],"not":[132],"possible":[133],"(cf.":[134,164],"[M.":[135,187],"Clausen,":[136],"A.":[137],"Dress,":[138],"J.":[139],"Grabmeier,":[140],"M.":[142,169,268],"Karpinski,":[143,170,269],"Theoret.":[144],"Comput.":[145],"Sci.,":[146],"1990,":[147],"appear]).":[149],"algorithm,":[151],"together":[152],"algorithms":[158],"characteristic":[162,232],"0":[163],"[D.":[165,264],"Yu.":[166,265],"Grigoriev":[167,266],"Proceedings":[172,193],"28th":[175],"IEEE":[176],"Symposium":[177,198],"on":[178,199],"Foundations":[180],"Computer":[182],"Science,":[183],"1987,":[184],"pp.":[185,205],"166\u2013172],":[186],"Ben-Or":[188],"P.":[190],"Tiwari,":[191],"20th":[196],"ACM":[197],"Theory":[201],"Computing,":[203],"1988,":[204],"301\u2013309]),":[206],"general":[213,277],"sparse":[215],"conversion":[216],"working":[218],"arbitrary":[220],"fields.":[221],"(The":[222],"reason":[223],"this":[225,238,242,252,310],"every":[228],"positive":[231],"contains":[233],"primitive":[235],"subfield":[236],"characteristic,":[239],"so":[241],"method":[243,255,278],"applied":[246],"slight":[249,298],"extension":[250,299,306],"subfield.)":[253],"solution":[257],"involves":[258],"enumeration":[261],"techniques":[262],"op.":[270],"cit.]":[271],"combined":[272],"introducing":[274],"new":[276],"solving":[280],"determining":[284],"identical":[290],"zero":[292],"by":[293],"evaluating":[294],"it":[295],"coefficient":[302],"whose":[307],"degree":[308],"logarithmic":[313],"nt).":[315]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
