{"id":"https://openalex.org/W4221162719","doi":"https://doi.org/10.1145/3476446.3536173","title":"Sparse Polynomial Interpolation and Division in Soft-linear Time","display_name":"Sparse Polynomial Interpolation and Division in Soft-linear Time","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4221162719","doi":"https://doi.org/10.1145/3476446.3536173"},"language":"en","primary_location":{"id":"doi:10.1145/3476446.3536173","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3536173","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2202.08106","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064771365","display_name":"Pascal Giorgi","orcid":"https://orcid.org/0000-0002-0489-5134"},"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"]},{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4405261681"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pascal Giorgi","raw_affiliation_strings":["LIRMM, Univ. Montpellier, CNRS, Montpellier, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIRMM, Univ. Montpellier, CNRS, Montpellier, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210101743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003590565","display_name":"Bruno Grenet","orcid":"https://orcid.org/0000-0003-2057-5429"},"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"]},{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4405261681"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bruno Grenet","raw_affiliation_strings":["LIRMM, Univ. Montpellier, CNRS, Montpellier, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIRMM, Univ. Montpellier, CNRS, Montpellier, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210101743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030554891","display_name":"Armelle Perret du Cray","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"]},{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]},{"id":"https://openalex.org/I4210101743","display_name":"Laboratoire d'Informatique, de Robotique et de Micro\u00e9lectronique de Montpellier","ror":"https://ror.org/013yean28","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I151295451","https://openalex.org/I19894307","https://openalex.org/I4210101743","https://openalex.org/I4210159245","https://openalex.org/I4405261681"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Armelle Perret du Cray","raw_affiliation_strings":["LIRMM, Univ. Montpellier, CNRS, Montpellier, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIRMM, Univ. Montpellier, CNRS, Montpellier, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210101743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029873080","display_name":"Daniel S. Roche","orcid":"https://orcid.org/0000-0003-1408-6872"},"institutions":[{"id":"https://openalex.org/I189158971","display_name":"United States Naval Academy","ror":"https://ror.org/00znex860","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I189158971","https://openalex.org/I3130687028"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel S. Roche","raw_affiliation_strings":["United States Naval Academy, Annapolis, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"United States Naval Academy, Annapolis, MD, USA","institution_ids":["https://openalex.org/I189158971"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8699,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.8457886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"459","last_page":"468"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","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/T11435","display_name":"Polynomial and algebraic computation","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/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7199559807777405},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.649280309677124},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5729894638061523},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5680978298187256},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5628690719604492},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4849815368652344},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4590446352958679},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.44248098134994507},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.4235539436340332},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40610939264297485},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.4032299518585205},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36082130670547485},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3296586871147156},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15332669019699097},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1347889006137848}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7199559807777405},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.649280309677124},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5729894638061523},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5680978298187256},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5628690719604492},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4849815368652344},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4590446352958679},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.44248098134994507},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.4235539436340332},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40610939264297485},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.4032299518585205},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36082130670547485},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3296586871147156},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15332669019699097},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1347889006137848},{"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/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3476446.3536173","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3476446.3536173","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2202.08106","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2202.08106","pdf_url":"https://arxiv.org/pdf/2202.08106","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:lirmm-03784815v1","is_oa":true,"landing_page_url":"https://hal-lirmm.ccsd.cnrs.fr/lirmm-03784815","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://www.issac-conference.org/2022/","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2202.08106","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2202.08106","pdf_url":"https://arxiv.org/pdf/2202.08106","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1583935850","https://openalex.org/W1783202385","https://openalex.org/W1941702124","https://openalex.org/W1965254799","https://openalex.org/W1969941659","https://openalex.org/W1978784845","https://openalex.org/W1991852511","https://openalex.org/W2001343527","https://openalex.org/W2015967265","https://openalex.org/W2022028092","https://openalex.org/W2022962368","https://openalex.org/W2026317840","https://openalex.org/W2028186291","https://openalex.org/W2031858455","https://openalex.org/W2033042165","https://openalex.org/W2040890430","https://openalex.org/W2044993127","https://openalex.org/W2065660785","https://openalex.org/W2071252649","https://openalex.org/W2072251416","https://openalex.org/W2096280747","https://openalex.org/W2100272829","https://openalex.org/W2100899126","https://openalex.org/W2113204179","https://openalex.org/W2113291984","https://openalex.org/W2113737071","https://openalex.org/W2126318803","https://openalex.org/W2140126816","https://openalex.org/W2143563649","https://openalex.org/W2144770505","https://openalex.org/W2163423227","https://openalex.org/W2818570966","https://openalex.org/W2888917571","https://openalex.org/W2913046577","https://openalex.org/W2959557165","https://openalex.org/W2980587714","https://openalex.org/W3003830892","https://openalex.org/W3018936433","https://openalex.org/W3045630729","https://openalex.org/W3101495262","https://openalex.org/W3102065507","https://openalex.org/W3133728983","https://openalex.org/W3179213994","https://openalex.org/W4234533504","https://openalex.org/W4254525706","https://openalex.org/W4386093834"],"related_works":["https://openalex.org/W4389457771","https://openalex.org/W2042172774","https://openalex.org/W1999125177","https://openalex.org/W2003738484","https://openalex.org/W4386147800","https://openalex.org/W4387722480","https://openalex.org/W2589218941","https://openalex.org/W2163356401","https://openalex.org/W3110405705","https://openalex.org/W2800722876"],"abstract_inverted_index":{"Given":[0],"a":[1,84,92,99,180],"way":[2,100],"to":[3,15,31,90,101],"evaluate":[4,102],"an":[5,24],"unknown":[6],"polynomial":[7,93],"with":[8,95,158,169],"integer":[9,96,170],"coefficients,":[10,66,171],"we":[11,26],"present":[12],"new":[13,85],"algorithms":[14],"recover":[16,91],"its":[17],"nonzero":[18,61],"coefficients":[19,97],"and":[20,71,111],"corresponding":[21],"exponents.":[22,188],"As":[23],"application,":[25],"adapt":[27],"this":[28,151],"interpolation":[29,156],"algorithm":[30,89,114,157],"the":[32,36,50,53,58,63,67,72,75,78,121,125,130,141,144,153,163,172,184,187],"problem":[33],"of":[34,39,49,52,60,65,69,74,80,124,143,186],"computing":[35],"exact":[37],"quotient":[38],"two":[40],"given":[41,98],"polynomials.":[42],"These":[43],"methods":[44],"are":[45],"efficient":[46],"in":[47,140,162],"terms":[48],"bit-length":[51,123,142,185],"sparse":[54,146,155],"representation,":[55],"that":[56,120],"is,":[57],"number":[59,68],"terms,":[62],"size":[64],"variables,":[70],"logarithm":[73],"degree.":[76],"At":[77],"core":[79],"our":[81,149],"results":[82,176],"is":[83,134,152],"Monte":[86],"Carlo":[87],"randomized":[88],"f(x)":[94],"f(\u03b8)":[103],"mod":[104],"m":[105],"for":[106],"any":[107],"chosen":[108],"integers":[109],"\u03b8":[110],"m.":[112],"This":[113],"has":[115],"nearly-optimal":[116],"bit":[117,160],"complexity,":[118],"meaning":[119],"total":[122,164],"probes,":[126],"as":[127,129],"well":[128],"computational":[131],"running":[132],"time,":[133],"softly":[135],"linear":[136],"(ignoring":[137],"logarithmic":[138],"factors)":[139],"resulting":[145],"polynomial.":[147],"To":[148],"knowledge,":[150],"first":[154],"soft-linear":[159],"complexity":[161],"output":[165],"size.":[166],"For":[167],"polynomials":[168],"best":[173],"previously":[174],"known":[175],"have":[177],"at":[178],"least":[179],"cubic":[181],"dependency":[182],"on":[183]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
