{"id":"https://openalex.org/W2082582261","doi":null,"title":"Lower Bounds for Testing Triangle-freeness in Boolean Functions","display_name":"Lower Bounds for Testing Triangle-freeness in Boolean Functions","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2082582261","mag":"2082582261"},"language":"en","primary_location":{"id":"pmh:oai:eprints.iisc.ac.in:51376","doi":null,"is_oa":false,"landing_page_url":"http://eprints.iisc.ac.in/51376/1/com_com-24_1_65_2015.pdf","pdf_url":"http://eprints.iisc.ac.in/51376/1/com_com-24_1_65_2015.pdf","source":{"id":"https://openalex.org/S4377196309","display_name":"NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"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/A5102919901","display_name":"Arnab Bhattacharyya","orcid":"https://orcid.org/0000-0002-3648-5957","observed_orcids":["https://orcid.org/0000-0002-3648-5957","https://orcid.org/0000-0002-3332-0700"]},"institutions":[{"id":"https://openalex.org/I4405258931","display_name":"MIT Computer Science and Artificial Intelligence Laboratory","ror":"https://ror.org/01e85r662","country_code":"US","type":"facility","lineage":["https://openalex.org/I4405258931","https://openalex.org/I63966007"]},{"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":false,"raw_author_name":"Arnab Bhattacharyya","raw_affiliation_strings":["CSAIL/MIT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CSAIL/MIT","institution_ids":["https://openalex.org/I4405258931","https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":null,"display_name":"Ning Xie","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4405258931","display_name":"MIT Computer Science and Artificial Intelligence Laboratory","ror":"https://ror.org/01e85r662","country_code":"US","type":"facility","lineage":["https://openalex.org/I4405258931","https://openalex.org/I63966007"]},{"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":false,"raw_author_name":"Ning Xie","raw_affiliation_strings":["CSAIL/MIT"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CSAIL/MIT","institution_ids":["https://openalex.org/I4405258931","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6503,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.87438337,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.49540001153945923,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.49540001153945923,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.3767000138759613,"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":0.010599999688565731,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-functions","display_name":"Boolean functions","score":0.8759999871253967},{"id":"https://openalex.org/keywords/query-complexity","display_name":"query complexity","score":0.8450000286102295},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.8360000252723694},{"id":"https://openalex.org/keywords/property-testing","display_name":"property testing","score":0.7950000166893005},{"id":"https://openalex.org/keywords/additive-combinatorics","display_name":"additive combinatorics","score":0.5400000214576721},{"id":"https://openalex.org/keywords/green-s-theorem","display_name":"Green's theorem","score":0.35600000619888306}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7279888391494751},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7018777132034302},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6421423554420471},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6265000104904175},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5827704668045044},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5637724995613098},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5366724133491516},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.533254086971283},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43898504972457886},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.42929011583328247},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.41970905661582947},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:eprints.iisc.ac.in:51376","doi":null,"is_oa":false,"landing_page_url":"http://eprints.iisc.ac.in/51376/1/com_com-24_1_65_2015.pdf","pdf_url":"http://eprints.iisc.ac.in/51376/1/com_com-24_1_65_2015.pdf","source":{"id":"https://openalex.org/S4377196309","display_name":"NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.184.8167","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.184.8167","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.csail.mit.edu/ningxie/papers/BX10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.215.4472","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.215.4472","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.siam.org/proceedings/soda/2010/SODA10_009_bhattacharyyaa.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.552.5116","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.552.5116","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.mit.edu/abhatt/www/QLBT_full.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.723.2225","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.723.2225","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.cis.fiu.edu/%7Enxie/papers/BX14.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1496801598","https://openalex.org/W1585475679","https://openalex.org/W1606480398","https://openalex.org/W1652781893","https://openalex.org/W1970630090","https://openalex.org/W1979740015","https://openalex.org/W1980424184","https://openalex.org/W1985538939","https://openalex.org/W2018925011","https://openalex.org/W2019367452","https://openalex.org/W2019475553","https://openalex.org/W2036501955","https://openalex.org/W2037773642","https://openalex.org/W2051880745","https://openalex.org/W2055194501","https://openalex.org/W2069200876","https://openalex.org/W2072288779","https://openalex.org/W2095273580","https://openalex.org/W2101060997","https://openalex.org/W2113121172","https://openalex.org/W2126296671","https://openalex.org/W2129465918","https://openalex.org/W2139374679","https://openalex.org/W2153063335","https://openalex.org/W2155600383","https://openalex.org/W2161620758","https://openalex.org/W2164542539","https://openalex.org/W2884506578","https://openalex.org/W2964194804","https://openalex.org/W3008660429","https://openalex.org/W3030488835","https://openalex.org/W3083751883","https://openalex.org/W4205302990"],"related_works":["https://openalex.org/W2169968099","https://openalex.org/W2964073278","https://openalex.org/W7099090532","https://openalex.org/W3183611787","https://openalex.org/W2593853527","https://openalex.org/W3161044530","https://openalex.org/W2042957148","https://openalex.org/W2064334110","https://openalex.org/W1988511047","https://openalex.org/W4416026818"],"abstract_inverted_index":{"Given":[0],"a":[1,11,19,141,216],"Boolean":[2],"function":[3,35,45,217],"f:":[4,218],"Fn2":[5,219],"\u2192":[6,220],"{0,":[7,221],"1},":[8],"we":[9,63,181],"say":[10],"triple":[12],"(x,":[13],"y,":[14],"x":[15,94],"+":[16,29,118],"y)":[17,30,119],"is":[18,53,140,147,176,229,259],"triangle":[20],"in":[21,149,159],"f":[22,40,52],"if":[23,136],"f(x)":[24,113],"=":[25,27,31,114,116,120],"f(y)":[26,106,115],"f(x":[28,117],"1.":[32,121],"A":[33,166],"triangle-free":[34,44,75,132,233],"contains":[36],"no":[37],"triangle.":[38],"If":[39],"differs":[41],"from":[42,58,77,80,102,131,231],"every":[43,198],"on":[46,172,224],"at":[47,100,260,283],"least":[48,261,284],"\u00b72n":[49],"points,":[50],"then":[51],"said":[54],"to":[55,163],"be":[56],"-far":[57,79,130,230],"triangle-free.":[59,81],"In":[60,178],"this":[61,179,273],"work,":[62],"analyze":[64],"the":[65,83,89,125,154,157,173,183,189,240,247,264,268],"query":[66,138,174,248,265],"complexity":[67,139,175,249,266],"of":[68,143,156,170,191,250,263,267],"testers":[69],"that,":[70,196],"with":[71,133],"constant":[72,134],"probability,":[73],"distinguish":[74],"functions":[76,129],"those":[78],"Let":[82],"canonical":[84,126,241,270],"tester":[85,127,256,278],"for":[86,188,197,209,239,257,279],"triangle-freeness":[87,258,280],"denote":[88],"algorithm":[90],"that":[91,124,208,246,275],"repeatedly":[92],"picks":[93],"and":[95,98,107,110,234],"y":[96],"uniformly":[97],"independently":[99],"random":[101],"Fn2,":[103],"queries":[104,192,238],"f(x),":[105],"f(x+":[108],"y),":[109],"checks":[111],"whether":[112],"Green":[122],"showed":[123],"rejects":[128],"probability":[135],"its":[137],"tower":[142,158],"2\u2019s":[144],"whose":[145],"height":[146,155],"polynomial":[148],"1/.":[150],"Fox":[151],"later":[152],"improved":[153],"Green\u2019s":[160],"upper":[161],"bound":[162,169,187],"O(log":[164],"1/).":[165],"trivial":[167],"lower":[168,186],"\u2126(1/)":[171],"immediate.":[177],"paper,":[180],"give":[182],"first":[184],"non-trivial":[185],"number":[190],"needed.":[193],"We":[194,243],"show":[195,245],"small":[199],"enough":[200],",":[201],"there":[202,214],"exists":[203,215],"an":[204],"integer":[205],"n0()":[206],"such":[207],"all":[210,225],"n":[211,226],"\u2265":[212],"n0":[213],"1}":[222],"depending":[223],"variables":[227],"which":[228],"being":[232],"requires":[235],"\u2126":[236,285],"(1/)4.847\u00b7\u00b7\u00b7":[237],"tester.":[242,271],"also":[244],"any":[251,276],"general":[252],"(possibly":[253],"adaptive)":[254],"one-sided":[255,277],"square-root":[262],"corresponding":[269],"Consequently,":[272],"means":[274],"must":[281],"make":[282],"(1/)2.423\u00b7\u00b7\u00b7":[286],"queries.":[287]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2016-06-24T00:00:00"}
