{"id":"https://openalex.org/W2154368141","doi":"https://doi.org/10.1137/0222062","title":"Learning Binary Relations and Total Orders","display_name":"Learning Binary Relations and Total Orders","publication_year":1993,"publication_date":"1993-10-01","ids":{"openalex":"https://openalex.org/W2154368141","doi":"https://doi.org/10.1137/0222062","mag":"2154368141"},"language":"en","primary_location":{"id":"doi:10.1137/0222062","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0222062","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/A5103351832","display_name":"Sally A. Goldman","orcid":null},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sally A. Goldman","raw_affiliation_strings":["Washington University St. Louis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Washington University St. Louis","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051087399","display_name":"Ronald L. Rivest","orcid":null},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald L. Rivest","raw_affiliation_strings":["Washington University St. Louis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Washington University St. Louis","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084108666","display_name":"Robert E. Schapire","orcid":"https://orcid.org/0000-0001-8616-1611"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert E. Schapire","raw_affiliation_strings":["Washington University St. Louis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Washington University St. Louis","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I204465549"],"apc_list":null,"apc_paid":null,"fwci":8.6893,"has_fulltext":false,"cited_by_count":67,"citation_normalized_percentile":{"value":0.97817833,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"5","first_page":"1006","last_page":"1034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","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/T12072","display_name":"Machine Learning and Algorithms","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/T12288","display_name":"Optimization and Search Problems","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9970999956130981,"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/logical-matrix","display_name":"Logical matrix","score":0.692878007888794},{"id":"https://openalex.org/keywords/binary-relation","display_name":"Binary relation","score":0.6406327486038208},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.5556198358535767},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5554050803184509},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5414441227912903},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5314100384712219},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.501690149307251},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4956701993942261},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.47737881541252136},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4740709364414215},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4575284421443939},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.44324997067451477},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4392533004283905},{"id":"https://openalex.org/keywords/mistake","display_name":"Mistake","score":0.4350994825363159},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4344109296798706},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4216562509536743},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.41439563035964966},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41239356994628906},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3614759147167206},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.1263582706451416},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12495312094688416}],"concepts":[{"id":"https://openalex.org/C163561899","wikidata":"https://www.wikidata.org/wiki/Q1994977","display_name":"Logical matrix","level":3,"score":0.692878007888794},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.6406327486038208},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.5556198358535767},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5554050803184509},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5414441227912903},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5314100384712219},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.501690149307251},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4956701993942261},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.47737881541252136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4740709364414215},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4575284421443939},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.44324997067451477},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4392533004283905},{"id":"https://openalex.org/C2777179996","wikidata":"https://www.wikidata.org/wiki/Q911222","display_name":"Mistake","level":2,"score":0.4350994825363159},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4344109296798706},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4216562509536743},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.41439563035964966},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41239356994628906},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3614759147167206},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.1263582706451416},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12495312094688416},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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:10.1137/0222062","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0222062","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":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1592882366","https://openalex.org/W1987679122","https://openalex.org/W1989445634","https://openalex.org/W2006912660","https://openalex.org/W2014603110","https://openalex.org/W2058947027","https://openalex.org/W2061496873","https://openalex.org/W2063342497","https://openalex.org/W2072370430","https://openalex.org/W2087907345","https://openalex.org/W2093825590","https://openalex.org/W2106285343","https://openalex.org/W2129113961","https://openalex.org/W2139709458","https://openalex.org/W2752885492","https://openalex.org/W3008609509","https://openalex.org/W4238893454","https://openalex.org/W4241497311"],"related_works":["https://openalex.org/W2379390860","https://openalex.org/W4287865815","https://openalex.org/W4307105233","https://openalex.org/W2990188275","https://openalex.org/W3006777378","https://openalex.org/W4241121725","https://openalex.org/W2113894890","https://openalex.org/W2351498809","https://openalex.org/W2364877460","https://openalex.org/W2904730515"],"abstract_inverted_index":{"The":[0,107,278],"problem":[1,185,229],"of":[2,10,29,35,44,62,110,122,140,167,181,186,217,230,238,245,247],"learning":[3,72,79,148,156,187,231],"a":[4,14,23,27,33,90,99,150,161,172,188,193,197,205,214,232,248,253,282],"binary":[5,24,73,189],"relation":[6,25,56,124,190],"between":[7,13,26,58],"two":[8,64],"sets":[9],"objects":[11],"or":[12,96,284],"set":[15,28,34,198],"and":[16,32,52,134],"itself":[17],"is":[18,49,192,199,221,225,291],"studied.":[19],"This":[20,223],"paper":[21,112,183],"represents":[22],"size":[30,36],"n":[31,265],"m":[37],"as":[38],"an":[39,76,94,239,272],"$n":[40],"\\times":[41],"m$":[42],"matrix":[43,121,151],"bits":[45],"whose":[46],"$(i,j)$":[47],"entry":[48],"1":[50],"if":[51,54],"only":[53],"the":[55,59,63,82,87,104,116,120,123,138,153,165,178,184,218,228,236,243,275,285,288],"holds":[57],"corresponding":[60],"elements":[61],"sets.":[65],"Polynomial":[66],"prediction":[67,141,144,255],"algorithms":[68],"are":[69,84],"presented":[70],"for":[71,115,241],"relations":[74],"in":[75,118,280],"extended":[77,154],"on-line":[78,155],"model,":[80],"where":[81],"examples":[83],"drawn":[85],"by":[86,89,93],"learner,":[88],"helpful":[91],"teacher,":[92],"adversary,":[95],"according":[97],"to":[98,212,227,251],"uniform":[100],"probability":[101,260],"distribution":[102],"on":[103,137,196],"instance":[105],"space.":[106],"first":[108],"part":[109,180],"this":[111,182],"presents":[113,132],"results":[114],"case":[117,279],"which":[119,281],"has":[125],"at":[126,262],"most":[127,263],"k":[128],"row":[129],"types.":[130],"It":[131],"upper":[133],"lower":[135],"bounds":[136,170],"number":[139,244],"mistakes":[142,270],"any":[143],"algorithm":[145,220,256],"makes":[146,261],"when":[147,271],"such":[149],"under":[152],"model.":[157],"Furthermore,":[158],"it":[159],"describes":[160],"technique":[162,203,224],"that":[163,191,257],"simplifies":[164],"proof":[166],"expected":[168],"mistake":[169],"against":[171],"randomly":[173],"chosen":[174],"query":[175,276,289],"sequence.":[176,277],"In":[177],"second":[179],"total":[194,233],"order":[195],"considered.":[200],"A":[201],"general":[202],"using":[204],"fully":[206],"polynomial":[207,254],"randomized":[208,215],"approximation":[209],"scheme":[210],"(fpras)":[211],"implement":[213],"version":[216],"halving":[219],"described.":[222],"applied":[226],"order,":[234,250],"through":[235],"use":[237],"fpras":[240],"counting":[242],"extensions":[246],"partial":[249],"obtain":[252],"with":[258],"high":[259],"$n\\lg":[264],"+":[266],"(\\lg":[267],"e)\\lg":[268],"n$":[269],"adversary":[273],"selects":[274,287],"teacher":[283],"learner":[286],"sequence":[290],"also":[292],"considered":[293]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}