{"id":"https://openalex.org/W2887208695","doi":"https://doi.org/10.1109/focs.2018.00059","title":"The Sketching Complexity of Graph and Hypergraph Counting","display_name":"The Sketching Complexity of Graph and Hypergraph Counting","publication_year":2018,"publication_date":"2018-10-01","ids":{"openalex":"https://openalex.org/W2887208695","doi":"https://doi.org/10.1109/focs.2018.00059","mag":"2887208695"},"language":"en","primary_location":{"id":"doi:10.1109/focs.2018.00059","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs.2018.00059","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1808.04995","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002326949","display_name":"John Kallaugher","orcid":"https://orcid.org/0000-0003-2591-3298"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Kallaugher","raw_affiliation_strings":["UT Austin, Austin, USA","The University of Texas at Austin, Austin, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UT Austin, Austin, USA","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"The University of Texas at Austin, Austin, United States","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086773451","display_name":"Michael Kapralov","orcid":"https://orcid.org/0009-0006-2882-0459"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Michael Kapralov","raw_affiliation_strings":["EPFL, Lausanne, Switzerland","\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EPFL, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083990461","display_name":"Eric Price","orcid":"https://orcid.org/0000-0002-3480-8054"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Price","raw_affiliation_strings":["UT Austin, Austin, USA","The University of Texas at Austin, Austin, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UT Austin, Austin, USA","institution_ids":["https://openalex.org/I86519309"]},{"raw_affiliation_string":"The University of Texas at Austin, Austin, United States","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6335,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62286658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"556","last_page":"567"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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":0.9994999766349792,"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/T12288","display_name":"Optimization and Search Problems","score":0.9983000159263611,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9976000189781189,"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/hypergraph","display_name":"Hypergraph","score":0.7474535703659058},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5212750434875488},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4952496588230133},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4674689769744873},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46631085872650146},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4278605580329895},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42370671033859253},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.4235290586948395},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42176252603530884},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.388070285320282},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36102569103240967}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.7474535703659058},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5212750434875488},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4952496588230133},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4674689769744873},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46631085872650146},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4278605580329895},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42370671033859253},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.4235290586948395},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42176252603530884},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.388070285320282},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36102569103240967},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/focs.2018.00059","is_oa":false,"landing_page_url":"https://doi.org/10.1109/focs.2018.00059","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1808.04995","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.04995","pdf_url":"https://arxiv.org/pdf/1808.04995","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2887208695","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1808.04995","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:infoscience.epfl.ch:263321","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/153816","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"conference proceedings"},{"id":"doi:10.48550/arxiv.1808.04995","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1808.04995","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1808.04995","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1808.04995","pdf_url":"https://arxiv.org/pdf/1808.04995","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":73,"referenced_works":["https://openalex.org/W1498019842","https://openalex.org/W1508887260","https://openalex.org/W1542957328","https://openalex.org/W1551652843","https://openalex.org/W1595640791","https://openalex.org/W1639030016","https://openalex.org/W1799685217","https://openalex.org/W1824295098","https://openalex.org/W1888346910","https://openalex.org/W1974332999","https://openalex.org/W1978676170","https://openalex.org/W1997010704","https://openalex.org/W2002205566","https://openalex.org/W2002576896","https://openalex.org/W2053182026","https://openalex.org/W2058851495","https://openalex.org/W2060385919","https://openalex.org/W2066811549","https://openalex.org/W2084170146","https://openalex.org/W2117848926","https://openalex.org/W2123033955","https://openalex.org/W2137778430","https://openalex.org/W2144146806","https://openalex.org/W2146492010","https://openalex.org/W2148488235","https://openalex.org/W2154191591","https://openalex.org/W2158432527","https://openalex.org/W2225286048","https://openalex.org/W2241571695","https://openalex.org/W2295466155","https://openalex.org/W2344844563","https://openalex.org/W2424986266","https://openalex.org/W2478210969","https://openalex.org/W2481330047","https://openalex.org/W2540367636","https://openalex.org/W2569757174","https://openalex.org/W2611566349","https://openalex.org/W2618062049","https://openalex.org/W2788362138","https://openalex.org/W2951669000","https://openalex.org/W2952096125","https://openalex.org/W2952116439","https://openalex.org/W2952341094","https://openalex.org/W2952627548","https://openalex.org/W2952674441","https://openalex.org/W2963001918","https://openalex.org/W2963034672","https://openalex.org/W2963827637","https://openalex.org/W2964156975","https://openalex.org/W2964259122","https://openalex.org/W3014147289","https://openalex.org/W3103185047","https://openalex.org/W4230053343","https://openalex.org/W4230889046","https://openalex.org/W4234540089","https://openalex.org/W4237171398","https://openalex.org/W4239886656","https://openalex.org/W4252630569","https://openalex.org/W6636606092","https://openalex.org/W6638398577","https://openalex.org/W6640581187","https://openalex.org/W6640913561","https://openalex.org/W6671071374","https://openalex.org/W6675283981","https://openalex.org/W6689557893","https://openalex.org/W6690388481","https://openalex.org/W6720341891","https://openalex.org/W6728989586","https://openalex.org/W6731348333","https://openalex.org/W6731766985","https://openalex.org/W6746057058","https://openalex.org/W6747920547","https://openalex.org/W6764720917"],"related_works":["https://openalex.org/W2963034672","https://openalex.org/W2779821190","https://openalex.org/W2767909715","https://openalex.org/W2902987863","https://openalex.org/W2949484202","https://openalex.org/W2946681422","https://openalex.org/W2104748762","https://openalex.org/W2025622191","https://openalex.org/W2604146837","https://openalex.org/W3156588038","https://openalex.org/W2767952030","https://openalex.org/W43914943","https://openalex.org/W2203972201","https://openalex.org/W3185251687","https://openalex.org/W3041708323","https://openalex.org/W3038109467","https://openalex.org/W3167661096","https://openalex.org/W2904738783","https://openalex.org/W2890468844","https://openalex.org/W1618327071"],"abstract_inverted_index":{"Subgraph":[0],"counting":[1,33,59,123,170],"is":[2,79,156],"a":[3,21,72,80,91,101,115,129,134,141,173,194,218],"fundamental":[4],"primitive":[5],"in":[6,11,38,61,95,133,193,209,232,258],"graph":[7,78,107,137,166],"processing,":[8],"with":[9,178,255],"applications":[10,231],"social":[12],"network":[13],"analysis":[14],"(e.g.,":[15],"estimating":[16],"the":[17,39,55,62,66,77,84,96,119,124,150,154,159,165,183,210,251],"clustering":[18],"coefficient":[19],"of":[20,31,74,83,93,122,126,128,143,153,164,186,197],"graph),":[22],"database":[23],"processing":[24],"and":[25,98,246],"other":[26,233],"areas.":[27],"The":[28],"space":[29,151,259],"complexity":[30,121,152],"subgraph":[32,56,131,169],"has":[34,88,99],"been":[35],"studied":[36],"extensively":[37],"literature,":[40,97],"but":[41],"many":[42],"natural":[43,174],"settings":[44],"are":[45,227],"still":[46],"not":[47],"well":[48],"understood.":[49],"In":[50,110],"this":[51,111],"paper":[52,112],"we":[53,113,147,202],"revisit":[54],"(and":[57],"hypergraph)":[58],"problem":[60,155],"sketching":[63,120],"model,":[64,213],"where":[65],"algorithm's":[67],"state":[68],"as":[69,140],"it":[70],"processes":[71],"stream":[73,142],"updates":[75],"to":[76,204,216,229,250],"linear":[81],"function":[82],"stream.":[85],"This":[86],"model":[87,103],"recently":[89],"received":[90],"lot":[92],"attention":[94],"become":[100],"standard":[102],"for":[104,239],"solving":[105],"dynamic":[106],"streaming":[108],"problems.":[109],"give":[114],"tight":[116,219,237],"bound":[117],"on":[118],"number":[125,163],"occurrences":[127],"small":[130],"H":[132],"bounded":[135],"degree":[136],"G":[138],"presented":[139],"edge":[144],"updates.":[145],"Specifically,":[146],"show":[148],"that":[149,201,224],"governed":[157,181],"by":[158,182],"fractional":[160],"vertex":[161,175,184],"cover":[162,185],"H.":[167,187],"Our":[168,188],"algorithm":[171,245],"implements":[172],"sampling":[176,179],"approach,":[177],"probabilities":[180],"main":[189],"technical":[190],"contribution":[191],"lies":[192],"new":[195],"set":[196],"Fourier":[198],"analytic":[199],"tools":[200],"develop":[203],"analyze":[205],"multiplayer":[206],"communication":[207,212],"protocols":[208],"simultaneous":[211],"allowing":[214],"us":[215],"prove":[217],"lower":[220,247],"bound.":[221],"We":[222],"believe":[223],"our":[225,244],"techniques":[226],"likely":[228],"find":[230],"settings.":[234],"Besides":[235],"giving":[236],"bounds":[238,248],"all":[240],"graphs":[241],"H,":[242],"both":[243],"extend":[249],"hypergraph":[252],"setting,":[253],"albeit":[254],"some":[256],"loss":[257],"complexity.":[260]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}