{"id":"https://openalex.org/W2161906179","doi":"https://doi.org/10.1137/110840741","title":"Testing and Reconstruction of Lipschitz Functions with Applications to Data Privacy","display_name":"Testing and Reconstruction of Lipschitz Functions with Applications to Data Privacy","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2161906179","doi":"https://doi.org/10.1137/110840741","mag":"2161906179"},"language":"en","primary_location":{"id":"doi:10.1137/110840741","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110840741","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-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/A5060771724","display_name":"Madhav Jha","orcid":"https://orcid.org/0000-0001-8528-4257"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Madhav Jha","raw_affiliation_strings":["Pennsylvania State University, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pennsylvania State University, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080839778","display_name":"Sofya Raskhodnikova","orcid":"https://orcid.org/0000-0002-4902-050X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sofya Raskhodnikova","raw_affiliation_strings":["Institute for Computational and Data Sciences (ICDS)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational and Data Sciences (ICDS)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.1033,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.95781224,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"42","issue":"2","first_page":"700","last_page":"731"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9998000264167786,"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":0.9990000128746033,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8488825559616089},{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.6493790745735168},{"id":"https://openalex.org/keywords/differential-privacy","display_name":"Differential privacy","score":0.6033620834350586},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6014145612716675},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5766400098800659},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5754671096801758},{"id":"https://openalex.org/keywords/lipschitz-domain","display_name":"Lipschitz domain","score":0.47318291664123535},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.43412038683891296},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4212004840373993},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.400814414024353},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3654188811779022},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24544447660446167},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23309633135795593}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8488825559616089},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.6493790745735168},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.6033620834350586},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6014145612716675},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5766400098800659},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5754671096801758},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.47318291664123535},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43412038683891296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4212004840373993},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.400814414024353},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3654188811779022},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24544447660446167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23309633135795593},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110840741","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110840741","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.4099999964237213,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G5050863863","display_name":"CAREER: Sublinear Algorithms --- Theory and Applications","funder_award_id":"0845701","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","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":26,"referenced_works":["https://openalex.org/W1528180898","https://openalex.org/W1970630090","https://openalex.org/W1980223785","https://openalex.org/W1983067233","https://openalex.org/W1986542077","https://openalex.org/W2012873258","https://openalex.org/W2016443407","https://openalex.org/W2018925011","https://openalex.org/W2026244324","https://openalex.org/W2031713274","https://openalex.org/W2036752160","https://openalex.org/W2069001533","https://openalex.org/W2069947312","https://openalex.org/W2070486524","https://openalex.org/W2071769989","https://openalex.org/W2073966617","https://openalex.org/W2091804135","https://openalex.org/W2100732817","https://openalex.org/W2105984887","https://openalex.org/W2107917944","https://openalex.org/W2116455242","https://openalex.org/W2141078756","https://openalex.org/W3023302315","https://openalex.org/W4235805661","https://openalex.org/W4241342151","https://openalex.org/W4249956697"],"related_works":["https://openalex.org/W2742067388","https://openalex.org/W4230778563","https://openalex.org/W2110693695","https://openalex.org/W4293718971","https://openalex.org/W2973109582","https://openalex.org/W4248060259","https://openalex.org/W960860267","https://openalex.org/W2083899393","https://openalex.org/W2055993960","https://openalex.org/W2406419904"],"abstract_inverted_index":{"A":[0,49,76],"function":[1,69,94,106,174,247],"$f":[2],":":[3],"D":[4],"\\to":[5],"R$":[6],"is":[7,167,206,256],"Lipschitz":[8,45,194,252],"if":[9],"$d_R(f(x),f(y))":[10],"\\leq":[11],"d_D(x,y)$":[12],"for":[13,134,244],"all":[14],"$x,y$":[15],"in":[16,87,178,208,219],"$D$,":[17],"where":[18,103],"$d_R$":[19],"and":[20,29,40,96,131,146,160,225],"$d_D$":[21],"denote":[22],"the":[23,27,36,44,57,71,88,104,109,119,139,170,200,209],"distance":[24],"metrics":[25],"on":[26,73,169,241],"range":[28],"domain":[30],"of":[31,38,43,47,138,176,181,189,196,202,215,254],"$f$,":[32,197],"respectively.":[33],"We":[34,127,234],"initiate":[35],"study":[37],"testing":[39],"local":[41,77,132,242],"reconstruction":[42],"property":[46,50,58,72,82],"functions.":[48],"tester":[51],"has":[52,118],"to":[53,125,157,165,192],"distinguish":[54],"functions":[55,64,135],"with":[56,70,143,187],"(in":[59,83],"this":[60,84],"case,":[61,85],"Lipschitz)":[62,86],"from":[63,67],"that":[65,172],"differ":[66],"every":[68],"many":[74],"values.":[75],"filter":[78],"reconstructs":[79],"a":[80,97,173,179,193,236,246,250,259],"desired":[81],"following":[89],"sense:":[90],"given":[91],"an":[92],"arbitrary":[93],"$f$":[95,112,117,175,248,255],"query":[98],"$x$,":[99],"it":[100],"returns":[101],"$g(x)$,":[102],"resulting":[105],"$g$":[107,121],"satisfies":[108],"property,":[110,120],"changing":[111],"only":[113],"when":[114,249],"necessary.":[115],"If":[116],"must":[122],"be":[123,185],"equal":[124],"$f$.":[126],"design":[128,154],"efficient":[129],"testers":[130],"reconstructors":[133],"over":[136],"domains":[137],"form":[140],"$\\{1,\\ldots,n\\}^d$,":[141],"equipped":[142],"$\\ell_1$":[144],"distance,":[145],"give":[147,235],"corresponding":[148],"impossibility":[149],"results.":[150],"The":[151,163],"algorithms":[152],"we":[153],"have":[155],"applications":[156],"program":[158],"analysis":[159],"data":[161,205],"privacy.":[162],"application":[164],"privacy":[166,201],"based":[168,240],"fact":[171],"entries":[177],"database":[180,210],"sensitive":[182],"information":[183],"can":[184],"released":[186],"noise":[188],"magnitude":[190],"proportional":[191],"constant":[195,253],"while":[198],"preserving":[199],"individuals":[203],"whose":[204],"stored":[207],"[Dwork":[211],"et":[212],"al.,":[213],"Theory":[214],"Cryptography,":[216],"Lecture":[217],"Notes":[218],"Comput.":[220],"Sci.":[221],"3878,":[222],"S.":[223],"Halevi":[224],"T.":[226],"Rabin,":[227],"eds.,":[228],"Springer,":[229],"Berlin,":[230],"2006,":[231],"pp.":[232],"265--284].":[233],"differentially":[237],"private":[238],"mechanism,":[239],"filters,":[243],"releasing":[245],"purported":[251],"provided":[257],"by":[258],"distrusted":[260],"client.":[261]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
