{"id":"https://openalex.org/W2169968099","doi":"https://doi.org/10.1145/2688073.2688084","title":"Sunflowers and Testing Triangle-Freeness of Functions","display_name":"Sunflowers and Testing Triangle-Freeness of Functions","publication_year":2015,"publication_date":"2015-01-11","ids":{"openalex":"https://openalex.org/W2169968099","doi":"https://doi.org/10.1145/2688073.2688084","mag":"2169968099"},"language":"en","primary_location":{"id":"doi:10.1145/2688073.2688084","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2688073.2688084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science","raw_type":"proceedings-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/A5020923873","display_name":"Ishay Haviv","orcid":"https://orcid.org/0000-0002-2903-076X"},"institutions":[{"id":"https://openalex.org/I4210141777","display_name":"Academic College of Tel Aviv-Yafo","ror":"https://ror.org/04cg6c004","country_code":"IL","type":"education","lineage":["https://openalex.org/I4210141777"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ishay Haviv","raw_affiliation_strings":["The Academic College of Tel Aviv-Yaffo, Tel Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Academic College of Tel Aviv-Yaffo, Tel Aviv, Israel","institution_ids":["https://openalex.org/I4210141777"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101646796","display_name":"Ning Xie","orcid":"https://orcid.org/0000-0003-3749-9207"},"institutions":[{"id":"https://openalex.org/I19700959","display_name":"Florida International University","ror":"https://ror.org/02gz6gg07","country_code":"US","type":"education","lineage":["https://openalex.org/I19700959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ning Xie","raw_affiliation_strings":["Florida International University, Miami, FL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Florida International University, Miami, FL, USA","institution_ids":["https://openalex.org/I19700959"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9074,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.9144427,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"357","last_page":"366"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9976999759674072,"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/T10237","display_name":"Cryptography and Data Security","score":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7324408292770386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7112517356872559},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6841750144958496},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5942426919937134},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5929628610610962},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4962611794471741},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.41849151253700256},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.41150736808776855},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14287406206130981},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08497563004493713}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7324408292770386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7112517356872559},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6841750144958496},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5942426919937134},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5929628610610962},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4962611794471741},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41849151253700256},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.41150736808776855},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14287406206130981},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08497563004493713},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2688073.2688084","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2688073.2688084","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.723.4694","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.723.4694","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/HX15.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.763.4644","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.763.4644","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1411.4692.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G3010388454","display_name":null,"funder_award_id":"CCF-1423034","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1482513610","https://openalex.org/W1483027031","https://openalex.org/W1513028911","https://openalex.org/W1540625694","https://openalex.org/W1599335667","https://openalex.org/W1653844607","https://openalex.org/W1970630090","https://openalex.org/W1977699786","https://openalex.org/W1979740015","https://openalex.org/W2012026677","https://openalex.org/W2012476164","https://openalex.org/W2013188591","https://openalex.org/W2016341899","https://openalex.org/W2016987856","https://openalex.org/W2018431582","https://openalex.org/W2018925011","https://openalex.org/W2023600080","https://openalex.org/W2032905283","https://openalex.org/W2037773642","https://openalex.org/W2038073775","https://openalex.org/W2039068037","https://openalex.org/W2048325432","https://openalex.org/W2055253799","https://openalex.org/W2072865951","https://openalex.org/W2082582261","https://openalex.org/W2095273580","https://openalex.org/W2101060997","https://openalex.org/W2124668680","https://openalex.org/W2126296671","https://openalex.org/W2143698439","https://openalex.org/W2153063335","https://openalex.org/W2161620758","https://openalex.org/W2164542539","https://openalex.org/W2169638123","https://openalex.org/W2170795229","https://openalex.org/W2963019803","https://openalex.org/W2964073278","https://openalex.org/W2964194804","https://openalex.org/W3102089577","https://openalex.org/W3138287827","https://openalex.org/W4233121052","https://openalex.org/W4238413586","https://openalex.org/W6637003139"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W4386900933","https://openalex.org/W4229058035","https://openalex.org/W3125672081","https://openalex.org/W2006389905","https://openalex.org/W4297797135","https://openalex.org/W2904666330"],"abstract_inverted_index":{"A":[0],"function":[1,76,94],"f":[2],":":[3],"Fn/2":[4,17],"\u2192":[5],"{0,1}":[6],"is":[7,39,71,90,110],"triangle-free":[8,45],"if":[9],"there":[10],"are":[11,50],"no":[12],"x1,":[13],"x2,":[14],"x3":[15,23],"\u2208":[16],"satisfying":[18],"x1":[19],"+":[20,22],"x2":[21],"--0":[24],"and":[25,113],"f(x1)":[26],"--":[27,29,31],"f(x2)":[28],"f(x3)":[30],"1.":[32],"In":[33],"testing":[34],"triangle":[35],"freeness,":[36],"the":[37,61,65,69,85,103,107],"goal":[38],"to":[40],"distinguish":[41],"with":[42],"high":[43],"probability":[44],"functions":[46],"from":[47,52],"those":[48],"which":[49],"\u03b5-far":[51],"being":[53],"triangle-free.":[54],"It":[55],"was":[56],"shown":[57],"by":[58,74],"Green":[59],"that":[60,77],"query":[62,104],"complexity":[63,105],"of":[64,95,106],"canonical":[66,108],"tester":[67,109],"for":[68],"problem":[70],"upper":[72,88],"bounded":[73],"a":[75,91],"depends":[78],"only":[79],"on":[80,102],"\u03b5":[81],"(GAFA,":[82],"2005),":[83],"however":[84],"best":[86,98],"known":[87,99],"bound":[89,101],"tower":[92],"type":[93],"1/\u03b5.":[96],"The":[97],"lower":[100],"1/\u03b513.239":[111],"(Fu":[112],"Kleinberg,":[114],"RANDOM,":[115],"2014).":[116]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}