{"id":"https://openalex.org/W1968818631","doi":"https://doi.org/10.1137/s0097539703422881","title":"Average-Case Performance of the Apriori Algorithm","display_name":"Average-Case Performance of the Apriori Algorithm","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1968818631","doi":"https://doi.org/10.1137/s0097539703422881","mag":"1968818631"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539703422881","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539703422881","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/A5030220389","display_name":"Paul W. Purdom","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paul W. Purdom","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110598353","display_name":"Dirk Van Gucht","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dirk Van Gucht","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112355304","display_name":"Dennis P. Groth","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dennis P. Groth","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5030220389"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.7731,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.95838127,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"33","issue":"5","first_page":"1223","last_page":"1260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9496999979019165,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9496999979019165,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.920799970626831,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/apriori-algorithm","display_name":"Apriori algorithm","score":0.7040590047836304},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6653650999069214},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5542200207710266},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5492619276046753},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.534946084022522},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5224834084510803},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.4278131425380707},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.42697200179100037},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34822750091552734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34563764929771423},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31554728746414185},{"id":"https://openalex.org/keywords/association-rule-learning","display_name":"Association rule learning","score":0.27991557121276855},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.24094322323799133},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0707504153251648}],"concepts":[{"id":"https://openalex.org/C81440476","wikidata":"https://www.wikidata.org/wiki/Q513511","display_name":"Apriori algorithm","level":3,"score":0.7040590047836304},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6653650999069214},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5542200207710266},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5492619276046753},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.534946084022522},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5224834084510803},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.4278131425380707},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.42697200179100037},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34822750091552734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34563764929771423},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31554728746414185},{"id":"https://openalex.org/C193524817","wikidata":"https://www.wikidata.org/wiki/Q386780","display_name":"Association rule learning","level":2,"score":0.27991557121276855},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.24094322323799133},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0707504153251648},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0097539703422881","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539703422881","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.23.369","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.369","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.indiana.edu/pub/techreports/TR529.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.550000011920929,"id":"https://metadata.un.org/sdg/8"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W62028356","https://openalex.org/W1484413656","https://openalex.org/W1495333347","https://openalex.org/W1570697393","https://openalex.org/W1584026429","https://openalex.org/W1983693613","https://openalex.org/W2011039300","https://openalex.org/W2023612196","https://openalex.org/W2037965136","https://openalex.org/W2042587503","https://openalex.org/W2064803206","https://openalex.org/W2064853889","https://openalex.org/W2085638007","https://openalex.org/W2125714474","https://openalex.org/W2141115288","https://openalex.org/W2210278139","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3034345083","https://openalex.org/W2351000793","https://openalex.org/W2366790077","https://openalex.org/W3133987543","https://openalex.org/W2355642745","https://openalex.org/W2384155583","https://openalex.org/W2372475599","https://openalex.org/W2383378197","https://openalex.org/W2357632367","https://openalex.org/W4388311650"],"abstract_inverted_index":{"The":[0,16,82,109,249],"failure":[1],"rate":[2],"of":[3,13,28,47,62,84,89,111,116,130,134,168,195,240,272,280,304],"the":[4,11,20,26,45,63,73,90,107,118,121,132,135,163,169,185,188,193,209,238,269,273,277,281,305,309],"Apriori":[5,21,136,210,310],"Algorithm":[6,22,137,211,311],"is":[7,23,86,95,113,138,143,152,162,171,231,244],"studied":[8],"analytically":[9],"for":[10,204,252,259],"case":[12],"random":[14,253],"shoppers.":[15],"time":[17],"needed":[18],"by":[19,25,308],"determined":[24],"number":[27,46,83,110,194],"item":[29,35,48,57,64,177,315],"sets":[30,36,49,58,178,265,292,316],"that":[31,37,50,94,125,317],"are":[32,51,180,255,266,284],"output":[33,55,98,214,243],"(successes:":[34],"occur":[38,66],"in":[39,67,77,313],"at":[40,68],"least":[41,69],"k":[42,70,80],"baskets)":[43],"and":[44,120,173,191,220],"counted":[52,179],"but":[53,72],"not":[54],"(failures:":[56],"where":[59,165],"all":[60,167,176,303],"subsets":[61],"set":[65,75],"baskets":[71],"full":[74],"occurs":[76],"less":[78],"than":[79,235],"baskets).":[81],"successes":[85,196],"a":[87,114,127,154,295],"property":[88,115],"data;":[91],"no":[92],"algorithm":[93,119],"required":[96],"to":[97,216,224,242,246],"each":[99],"success":[100],"can":[101],"avoid":[102],"doing":[103],"work":[104,170,222,241,306],"associated":[105],"with":[106,157,187],"successes.":[108],"failures":[112],"both":[117],"data.":[122],"We":[123],"find":[124],"under":[126,145,299],"wide":[128],"range":[129],"conditions":[131,301],"performance":[133],"almost":[139],"as":[140,142],"bad":[141,155,296],"permitted":[144],"sophisticated":[146],"worst-case":[147],"analyses.":[148],"In":[149,228,275],"particular,":[150,276],"there":[151],"usually":[153,232],"level":[156,164,186,198],"two":[158],"properties:":[159],"(1)":[160],"it":[161],"nearly":[166,175,302],"done,":[172],"(2)":[174],"failures.":[181],"Let":[182],"l":[183,199],"be":[184,200],"most":[189,288,300],"successes,":[190],"let":[192],"on":[197],"approximately":[201,217,225,247],"${m\\choose":[202,218,226],"l}$":[203,219],"some":[205],"m.":[206],"Then,":[207],"typically,":[208],"has":[212],"total":[213,221],"proportional":[215,223,245],"l+1}$.":[227],"addition":[229],"m":[230],"much":[233],"larger":[234],"l,":[236],"so":[237],"ratio":[239],"$m/(l+1)$.":[248],"analytical":[250],"results":[251],"shoppers":[254,283],"compared":[256],"against":[257],"measurements":[258],"three":[260],"data":[261,264,291],"sets.":[262],"These":[263],"more":[267],"like":[268],"usual":[270],"applications":[271],"algorithm.":[274],"buying":[278],"patterns":[279],"various":[282],"highly":[285],"correlated.":[286],"For":[287],"thresholds,":[289],"these":[290],"also":[293],"have":[294],"level.":[297],"Thus,":[298],"done":[307],"consists":[312],"counting":[314],"fail.":[318]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":7},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}