{"id":"https://openalex.org/W1566281515","doi":"https://doi.org/10.1007/3-540-16078-7_69","title":"Polynomial time algorithms for finding integer relations among real numbers","display_name":"Polynomial time algorithms for finding integer relations among real numbers","publication_year":1986,"publication_date":"1986-01-01","ids":{"openalex":"https://openalex.org/W1566281515","doi":"https://doi.org/10.1007/3-540-16078-7_69","mag":"1566281515"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-16078-7_69","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-16078-7_69","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5013166918","display_name":"Johan H\u00e5stad","orcid":"https://orcid.org/0000-0002-5379-345X"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Hastad","raw_affiliation_strings":["Department of Computer Science, MIT, Cambridge, Massachusetts"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, MIT, Cambridge, Massachusetts","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029018143","display_name":"Bettina Helfrich","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"B. Helfrich","raw_affiliation_strings":["Fachbereich Mathematik/Informatik, Universit\u00e4t Frankfurt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik/Informatik, Universit\u00e4t Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005612207","display_name":"Jeffrey C. Lagarias","orcid":"https://orcid.org/0000-0002-4157-5527"},"institutions":[{"id":"https://openalex.org/I1283103587","display_name":"AT&T (United States)","ror":"https://ror.org/02bbd5539","country_code":"US","type":"company","lineage":["https://openalex.org/I1283103587"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Lagarias","raw_affiliation_strings":["Bell Laboratories, AT&T, Murray Hill, New Jersey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Laboratories, AT&T, Murray Hill, New Jersey","institution_ids":["https://openalex.org/I1283103587"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111598509","display_name":"C. P. Schnorr","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"C. P. Schnorr","raw_affiliation_strings":["Fachbereich Mathematik/Informatik, Universit\u00e4t Frankfurt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik/Informatik, Universit\u00e4t Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":5.3558,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.96993007,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"105","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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/T11567","display_name":"semigroups and automata theory","score":0.9994000196456909,"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":0.9991999864578247,"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/integer","display_name":"Integer (computer science)","score":0.7584711313247681},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.6679350137710571},{"id":"https://openalex.org/keywords/lattice-reduction","display_name":"Lattice reduction","score":0.5428947806358337},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5117003917694092},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.5048969388008118},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4851277768611908},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.484094500541687},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"Integer lattice","score":0.4490101635456085},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4278390407562256},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.41927361488342285},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.41175174713134766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4085233211517334},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37460124492645264}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7584711313247681},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.6679350137710571},{"id":"https://openalex.org/C44274781","wikidata":"https://www.wikidata.org/wiki/Q6497132","display_name":"Lattice reduction","level":4,"score":0.5428947806358337},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5117003917694092},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.5048969388008118},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4851277768611908},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.484094500541687},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.4490101635456085},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4278390407562256},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41927361488342285},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41175174713134766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4085233211517334},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37460124492645264},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.0},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-16078-7_69","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-16078-7_69","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2022213653","https://openalex.org/W2040569180","https://openalex.org/W2047328744","https://openalex.org/W2124783843","https://openalex.org/W2141040012","https://openalex.org/W4248002299"],"related_works":["https://openalex.org/W4287101864","https://openalex.org/W4323555821","https://openalex.org/W2801334986","https://openalex.org/W4376639581","https://openalex.org/W107540463","https://openalex.org/W2007777736","https://openalex.org/W1662485015","https://openalex.org/W2034259951","https://openalex.org/W2111416661","https://openalex.org/W2092901733"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}