{"id":"https://openalex.org/W2156516305","doi":"https://doi.org/10.1145/103516.103522","title":"A lower bound for integer greatest common divisor computations","display_name":"A lower bound for integer greatest common divisor computations","publication_year":1991,"publication_date":"1991-04-01","ids":{"openalex":"https://openalex.org/W2156516305","doi":"https://doi.org/10.1145/103516.103522","mag":"2156516305"},"language":"en","primary_location":{"id":"doi:10.1145/103516.103522","is_oa":true,"landing_page_url":"https://doi.org/10.1145/103516.103522","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/103516.103522","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/10.1145/103516.103522","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014637159","display_name":"Yishay Mansour","orcid":"https://orcid.org/0000-0001-6891-2645"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yishay Mansour","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089964489","display_name":"Baruch Schieber","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Baruch Schieber","raw_affiliation_strings":["IBM T. J. Watson Research Center, Yorktown Heights, NY"],"affiliations":[{"raw_affiliation_string":"IBM T. J. Watson Research Center, Yorktown Heights, NY","institution_ids":["https://openalex.org/I4210114115"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100820614","display_name":"Prasoon Tiwari","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Prasoon Tiwari","raw_affiliation_strings":["IBM T. J. Watson Research Center, Yorktown Heights, NY"],"affiliations":[{"raw_affiliation_string":"IBM T. J. Watson Research Center, Yorktown Heights, NY","institution_ids":["https://openalex.org/I4210114115"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014637159"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":1.9867,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.87575758,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"38","issue":"2","first_page":"453","last_page":"471"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","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"}}],"keywords":[{"id":"https://openalex.org/keywords/greatest-common-divisor","display_name":"Greatest common divisor","score":0.8839331865310669},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7673935890197754},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.688050389289856},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6857515573501587},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6849441528320312},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6460828185081482},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5865265130996704},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5732517242431641},{"id":"https://openalex.org/keywords/divisor","display_name":"Divisor (algebraic geometry)","score":0.5610525012016296},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.550342321395874},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5443134307861328},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16280919313430786},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12360462546348572}],"concepts":[{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.8839331865310669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7673935890197754},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.688050389289856},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6857515573501587},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6849441528320312},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6460828185081482},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5865265130996704},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5732517242431641},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.5610525012016296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.550342321395874},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5443134307861328},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16280919313430786},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12360462546348572},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/103516.103522","is_oa":true,"landing_page_url":"https://doi.org/10.1145/103516.103522","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/103516.103522","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:10.1145/103516.103522","is_oa":true,"landing_page_url":"https://doi.org/10.1145/103516.103522","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/103516.103522","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2156516305.pdf","grobid_xml":"https://content.openalex.org/works/W2156516305.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W129807151","https://openalex.org/W220172787","https://openalex.org/W1508811963","https://openalex.org/W1519444547","https://openalex.org/W1536248371","https://openalex.org/W1969096587","https://openalex.org/W1975154469","https://openalex.org/W1994398507","https://openalex.org/W1999773905","https://openalex.org/W2002158735","https://openalex.org/W2010811692","https://openalex.org/W2033260394","https://openalex.org/W2044850435","https://openalex.org/W2059985428","https://openalex.org/W2063243181","https://openalex.org/W2078612732","https://openalex.org/W2088300760","https://openalex.org/W2100440346","https://openalex.org/W2151358049","https://openalex.org/W2561675875","https://openalex.org/W2752061190","https://openalex.org/W2752853835","https://openalex.org/W4250775169","https://openalex.org/W6633749307"],"related_works":["https://openalex.org/W2947649114","https://openalex.org/W2492714232","https://openalex.org/W2111425413","https://openalex.org/W2963207021","https://openalex.org/W2038038783","https://openalex.org/W2019745071","https://openalex.org/W4287629074","https://openalex.org/W3095434007","https://openalex.org/W4297433722","https://openalex.org/W2074247864"],"abstract_inverted_index":{"It":[0],"is":[1,30,113,134],"proved":[2,157],"that":[3,104],"no":[4],"finite":[5],"computation":[6,92],"tree":[7,62,93],"with":[8,94],"operations":[9,95],"{":[10,96],"+,":[11,97],"-,":[12,98],"*,":[13,99],"/,":[14,100],"mod,":[15,101],"<":[16,102],"}":[17,103],"can":[18],"decide":[19],"whether":[20,106],"the":[21,52,61,88,107,131,137],"greatest":[22],"common":[23],"divisor":[24],"(gcd)":[25],"of":[26,35,90,109,118,139,154],"a":[27,37,43,110,122,144,151,159],"and":[28,38,68,111,123],"b":[29,39,112,124],"one,":[31,114],"for":[32,115,129,150],"all":[33,116],"pairs":[34,117],"integers":[36,121],".":[40,125],"This":[41],"settles":[42],"problem":[44],"posed":[45],"by":[46],"Gro\u00a8tschel":[47],"et":[48],"al.":[49],"Moreover,":[50],"if":[51],"constants":[53],"explicitly":[54],"involved":[55],"in":[56,60,136],"any":[57,71,91],"operation":[58,133],"performed":[59],"are":[63,156],"restricted":[64],"to":[65],"be":[66,75],"\u201c0\u201d":[67],"\u201c1\u201d":[69],"(and":[70],"other":[72,147],"constant":[73],"must":[74],"computed),":[76],"then":[77],"we":[78],"prove":[79],"an":[80],"\u03a9(log":[81],"log":[82],"n":[83,119],")":[84],"lower":[85,141,148],"bound":[86],"on":[87],"depth":[89],"decides":[105],"gcd":[108],"-bit":[120],"A":[126],"novel":[127],"technique":[128],"handling":[130],"truncation":[132],"implicit":[135],"proof":[138],"this":[140],"bound.":[142],"In":[143],"companion":[145],"paper,":[146],"bounds":[149],"large":[152],"class":[153],"problems":[155],"using":[158],"similar":[160],"technique.":[161]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}