{"id":"https://openalex.org/W2424986266","doi":"https://doi.org/10.1145/2902251.2902283","title":"Better Algorithms for Counting Triangles in Data Streams","display_name":"Better Algorithms for Counting Triangles in Data Streams","publication_year":2016,"publication_date":"2016-06-15","ids":{"openalex":"https://openalex.org/W2424986266","doi":"https://doi.org/10.1145/2902251.2902283","mag":"2424986266"},"language":"en","primary_location":{"id":"doi:10.1145/2902251.2902283","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2902251.2902283","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2902283&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://dl.acm.org/ft_gateway.cfm?id=2902283&type=pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101979548","display_name":"Andrew McGregor","orcid":"https://orcid.org/0000-0002-2124-160X"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew McGregor","raw_affiliation_strings":["University of Massachusetts Amherst, Amherst, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Massachusetts Amherst, Amherst, USA","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041251603","display_name":"Sofya Vorotnikova","orcid":"https://orcid.org/0000-0002-3035-1122"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sofya Vorotnikova","raw_affiliation_strings":["University of Massachusetts Amherst, Amherst, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Massachusetts Amherst, Amherst, USA","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034746607","display_name":"Hoa T. Vu","orcid":"https://orcid.org/0000-0001-8873-0208"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hoa T. Vu","raw_affiliation_strings":["University of Massachusetts Amherst, Amherst, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Massachusetts Amherst, Amherst, USA","institution_ids":["https://openalex.org/I24603500"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I24603500"],"apc_list":null,"apc_paid":null,"fwci":4.4617,"has_fulltext":true,"cited_by_count":71,"citation_normalized_percentile":{"value":0.96149792,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"401","last_page":"411"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12761","display_name":"Data Stream Mining Techniques","score":0.9980000257492065,"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/T12761","display_name":"Data Stream Mining Techniques","score":0.9980000257492065,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9876999855041504,"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/T10317","display_name":"Advanced Database Systems and Queries","score":0.9869999885559082,"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/adjacency-list","display_name":"Adjacency list","score":0.7180220484733582},{"id":"https://openalex.org/keywords/streaming-algorithm","display_name":"Streaming algorithm","score":0.6464874148368835},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5488581657409668},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5422803163528442},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.5070986747741699},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4905907213687897},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48222267627716064},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47301533818244934},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4632391333580017},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.43414008617401123},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.4283674359321594},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.41127389669418335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35995781421661377}],"concepts":[{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.7180220484733582},{"id":"https://openalex.org/C187166803","wikidata":"https://www.wikidata.org/wiki/Q2835831","display_name":"Streaming algorithm","level":3,"score":0.6464874148368835},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5488581657409668},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5422803163528442},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.5070986747741699},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4905907213687897},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48222267627716064},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47301533818244934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4632391333580017},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.43414008617401123},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.4283674359321594},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41127389669418335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35995781421661377},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2902251.2902283","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2902251.2902283","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2902283&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/2902251.2902283","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2902251.2902283","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2902283&type=pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems","raw_type":"proceedings-article"},"sustainable_development_goals":[{"score":0.4099999964237213,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2844836911","display_name":"AF: Small: Massive Graph Analysis via Linear Measurements: Towards a Theory of Homomorphic Co","funder_award_id":"1320719","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6029386486","display_name":"CAREER: New Directions for Sketching and Stream Computation","funder_award_id":"0953754","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7223291013","display_name":"BIGDATA: Small: DA: Collaborative Research: From Data To Users: Providing Interpretable and Verifiable Explanations in Data Mining","funder_award_id":"1251110","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2424986266.pdf","grobid_xml":"https://content.openalex.org/works/W2424986266.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W1485437584","https://openalex.org/W1498019842","https://openalex.org/W1542957328","https://openalex.org/W1551652843","https://openalex.org/W1595409123","https://openalex.org/W1595640791","https://openalex.org/W1614522028","https://openalex.org/W1639030016","https://openalex.org/W1799685217","https://openalex.org/W1967066104","https://openalex.org/W1986745018","https://openalex.org/W1991099830","https://openalex.org/W1997010704","https://openalex.org/W2001125165","https://openalex.org/W2002205566","https://openalex.org/W2002576896","https://openalex.org/W2016289973","https://openalex.org/W2020022171","https://openalex.org/W2049661027","https://openalex.org/W2055245094","https://openalex.org/W2059867647","https://openalex.org/W2060385919","https://openalex.org/W2069414131","https://openalex.org/W2084170146","https://openalex.org/W2093063455","https://openalex.org/W2094308804","https://openalex.org/W2101157403","https://openalex.org/W2110814195","https://openalex.org/W2110942501","https://openalex.org/W2116759966","https://openalex.org/W2117071406","https://openalex.org/W2119885577","https://openalex.org/W2123033955","https://openalex.org/W2144146806","https://openalex.org/W2151078464","https://openalex.org/W2153624566","https://openalex.org/W2154191591","https://openalex.org/W2245672739","https://openalex.org/W2260890852","https://openalex.org/W2347145740","https://openalex.org/W2493333348","https://openalex.org/W2884439552","https://openalex.org/W2950428309","https://openalex.org/W2950562895","https://openalex.org/W3103185047","https://openalex.org/W3183766709","https://openalex.org/W4230053343","https://openalex.org/W6636207504","https://openalex.org/W6692506595","https://openalex.org/W6731710649"],"related_works":["https://openalex.org/W4213150077","https://openalex.org/W2369410163","https://openalex.org/W2059018062","https://openalex.org/W2604585036","https://openalex.org/W2078477160","https://openalex.org/W1989103179","https://openalex.org/W1991172810","https://openalex.org/W125803343","https://openalex.org/W2153421018","https://openalex.org/W2117632582"],"abstract_inverted_index":{"We":[0,122],"present":[1],"space-efficient":[2],"data":[3],"stream":[4,94],"algorithms":[5],"for":[6,220],"approximating":[7],"the":[8,47,53,69,75,85,87,93,97,100,106,117,125,128,135,159,166,191,200,208,217],"number":[9,54,70,76],"of":[10,41,52,55,71,77,96,99,127,246],"triangles":[11,56],"in":[12,35,50,84,91,102,111,131,147,155,207],"a":[13,17,28,38,59],"graph":[14,29,101],"up":[15],"to":[16,116,190,197,204],"factor":[18],"1+\u03b5.":[19],"While":[20],"it":[21],"can":[22,228],"be":[23,229,245],"shown":[24],"that":[25,142,172,180,224],"determining":[26],"whether":[27],"is":[30,32,145,153,238],"triangle-free":[31],"not":[33],"possible":[34],"sub-linear":[36],"space,":[37],"large":[39],"body":[40],"work":[42],"has":[43],"focused":[44],"on":[45,62],"minimizing":[46],"space":[48,144,152,174,182],"required":[49],"terms":[51],"T":[57],"(or":[58],"lower":[60],"bound":[61],"this":[63,236,242],"quantity)":[64],"and":[65,74,105,150,179,187,241],"other":[66],"parameters":[67],"including":[68],"nodes":[72],"n":[73],"edges":[78,98,114],"m.":[79],"Two":[80],"models":[81],"are":[82],"important":[83],"literature:":[86],"arbitrary":[88,103,167,209],"order":[89,104,109,138,168,210],"model":[90,110],"which":[92,112],"consists":[95],"adjacency":[107,136],"list":[108,137],"all":[113],"incident":[115],"same":[118],"node":[119],"appear":[120],"consecutively.":[121],"improve":[123],"over":[124],"state":[126],"art":[129],"results":[130],"both":[132],"models.":[133],"For":[134,165],"model,":[139,169],"we":[140,170,194,215],"show":[141,171,195],"~O(\u03b5-2m/\u221aT)":[143,173],"sufficient":[146,154],"one":[148],"pass":[149],"~O(\u03b5-2m3/2/T)":[151,181],"two":[156,177],"passes":[157,178,186],"where":[158],"~O(\u00b7)":[160],"notation":[161],"suppresses":[162],"log":[163],"factors.":[164],"suffices":[175,183],"given":[176,184],"three":[185],"oracle":[188],"access":[189],"degrees.":[192],"Finally,":[193],"how":[196],"efficiently":[198],"implement":[199],"\"wedge":[201],"sampling\"":[202],"approach":[203],"triangle":[205],"estimation":[206],"model.":[211],"To":[212],"do":[213],"this,":[214],"develop":[216],"first":[218],"algorithm":[219],"lp":[221],"sampling":[222],"such":[223],"multiple":[225],"independent":[226,247],"samples":[227],"generated":[230],"with":[231],"O(polylog":[232],"n)":[233],"update":[234],"time;":[235],"primitive":[237],"widely":[239],"applicable":[240],"result":[243],"may":[244],"interest.":[248]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}