{"id":"https://openalex.org/W7164496051","doi":"https://doi.org/10.48550/arxiv.2606.13182","title":"Sketching Intersection Profiles: A Simple Proof and Three Applications","display_name":"Sketching Intersection Profiles: A Simple Proof and Three Applications","publication_year":2026,"publication_date":"2026-06-11","ids":{"openalex":"https://openalex.org/W7164496051","doi":"https://doi.org/10.48550/arxiv.2606.13182"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.13182","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13182","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.13182","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078401676","display_name":"Flavio Chierichetti","orcid":"https://orcid.org/0000-0001-8261-9058"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chierichetti, Flavio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013240704","display_name":"M. Giacchini","orcid":"https://orcid.org/0009-0009-5704-098X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giacchini, Mirko","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138552422","display_name":"Ravi Kumar","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kumar, Ravi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063633119","display_name":"Alessandro Panconesi","orcid":"https://orcid.org/0000-0002-2169-3067"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Panconesi, Alessandro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138516529","display_name":"Erasmo Tani","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tani, Erasmo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137616153","display_name":"Andrew Tomkins","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tomkins, Andrew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.6098999977111816,"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":0.6098999977111816,"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":0.0502999983727932,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.03220000118017197,"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7682999968528748},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6696000099182129},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6412000060081482},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.5756999850273132},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5576000213623047},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5037000179290771},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5016999840736389},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.43230000138282776}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7682999968528748},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6696000099182129},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6471999883651733},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6412000060081482},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5756999850273132},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5576000213623047},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5037000179290771},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5016999840736389},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48100000619888306},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.453900009393692},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43230000138282776},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4196000099182129},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.3578000068664551},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3224000036716461},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31029999256134033},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.25839999318122864}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.13182","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13182","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"doi:10.48550/arxiv.2606.13182","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13182","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.5998175740242004,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1,147],"work":[2],"we":[3,110,172],"settle":[4],"the":[5,29,68,72,96,100,125,155,179,186,190,203],"complexity":[6,31],"of":[7,32,44,98,103],"three":[8],"sketching":[9,15,33,47,63,99,182],"problems.":[10],"(i)":[11],"We":[12,37,56],"show":[13],"that":[14],"vertex":[16],"neighborhood":[17],"sizes":[18],"in":[19,25,160,185,188,207],"graphs":[20],"requires":[21],"$\u03a9(n^2)$":[22,59],"bits,":[23],"standing":[24],"sharp":[26],"contrast":[27],"to":[28,84,134],"$\\tilde{O}(n)$":[30],"edge":[34],"cuts.":[35],"(ii)":[36],"obtain":[38,143],"tight":[39,164],"lower":[40,60,144,183],"and":[41,52,78],"upper":[42,82],"bounds":[43,89,145,165],"$\\tilde\u0398(n^2)$":[45],"for":[46,62,117,146,162,178],"coverage":[48],"functions":[49],"with":[50,95],"additive":[51,139],"multiplicative":[53],"errors.":[54],"(iii)":[55],"prove":[57],"an":[58,169,175],"bound":[61,77,83],"Random":[64],"Utility":[65],"Models":[66],"under":[67],"$\\ell_\\infty$-norm,":[69],"improving":[70],"upon":[71],"previous":[73,208],"$\u03a9(n":[74],"\\log":[75],"n)$":[76],"matching":[79],"a":[80,93,104,112,136],"known":[81,152],"within":[85,135],"logarithmic":[86],"factors.":[87],"These":[88],"are":[90,166],"obtained":[91],"through":[92],"connection":[94],"problem":[97,149,159],"intersection":[101,180],"profile":[102,181],"distribution":[105],"$D$":[106],"on":[107,199],"$2^{[n]}$.":[108],"Specifically,":[109],"seek":[111],"succinct":[113],"data":[114],"structure":[115],"that,":[116],"any":[118],"query":[119],"set":[120],"$S":[121],"\\subseteq":[122],"[n]$,":[123],"approximates":[124],"quantity":[126],"$\\Pr_{T":[127],"\\sim":[128],"D}[T":[129],"\\cap":[130],"S":[131],"\\neq":[132],"\\varnothing]$":[133],"small":[137],"constant":[138],"error.":[140],"One":[141],"can":[142],"latter":[148],"directly":[150],"from":[151],"results":[153],"about":[154],"itemset":[156],"frequency":[157],"estimation":[158],"databases":[161],"which":[163,189],"known.":[167],"As":[168],"additional":[170],"contribution,":[171],"also":[173],"provide":[174],"alternative":[176],"proof":[177,196],"bound,":[184],"setting":[187],"accuracy":[191],"parameter":[192],"is":[193],"constant.":[194],"This":[195],"relies":[197],"solely":[198],"elementary":[200],"probability":[201],"avoiding":[202],"heavier":[204],"machinery":[205],"used":[206],"proofs.":[209]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-13T00:00:00"}