{"id":"https://openalex.org/W2137615848","doi":"https://doi.org/10.1137/15m1017958","title":"Sketching and Embedding are Equivalent for Norms","display_name":"Sketching and Embedding are Equivalent for Norms","publication_year":2015,"publication_date":"2015-06-03","ids":{"openalex":"https://openalex.org/W2137615848","doi":"https://doi.org/10.1137/15m1017958","mag":"2137615848"},"language":"en","primary_location":{"id":"doi:10.1137/15m1017958","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1017958","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1411.2577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088346829","display_name":"Alexandr Andoni","orcid":"https://orcid.org/0009-0004-8042-0976"},"institutions":[{"id":"https://openalex.org/I4210107338","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexandr Andoni","raw_affiliation_strings":["Simons Institute, UC Berkeley, Berkeley, CA, USA"],"affiliations":[{"raw_affiliation_string":"Simons Institute, UC Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I4210107338","https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037378898","display_name":"Robert Krauthgamer","orcid":"https://orcid.org/0009-0003-8154-3735"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Robert Krauthgamer","raw_affiliation_strings":["Weizmann Institute, Rehovot, Israel"],"affiliations":[{"raw_affiliation_string":"Weizmann Institute, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056565460","display_name":"Ilya Razenshteyn","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ilya Razenshteyn","raw_affiliation_strings":["MIT, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210110987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088346829"],"corresponding_institution_ids":["https://openalex.org/I4210107338","https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":1.774,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.8700168,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"47","issue":"3","first_page":"479","last_page":"488"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9973000288009644,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9969000220298767,"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/embedding","display_name":"Embedding","score":0.8027694225311279},{"id":"https://openalex.org/keywords/converse","display_name":"Converse","score":0.7925329208374023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7202451229095459},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6135416030883789},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5923036932945251},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4876478910446167},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4487428367137909},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4274170398712158},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14882627129554749},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0736268162727356}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.8027694225311279},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.7925329208374023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7202451229095459},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6135416030883789},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5923036932945251},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4876478910446167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4487428367137909},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4274170398712158},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14882627129554749},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0736268162727356},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1017958","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1017958","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"},{"id":"doi:10.1145/2746539.2746552","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2746539.2746552","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1411.2577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.2577","pdf_url":"https://arxiv.org/pdf/1411.2577","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"mag:2137615848","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1411.2577.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1411.2577","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1411.2577","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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1411.2577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.2577","pdf_url":"https://arxiv.org/pdf/1411.2577","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G173099627","display_name":null,"funder_award_id":"#897/13","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G8331198436","display_name":null,"funder_award_id":"2010418","funder_id":"https://openalex.org/F4320308960","funder_display_name":"United States - Israel Binational Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320308960","display_name":"United States - Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2137615848.pdf","grobid_xml":"https://content.openalex.org/works/W2137615848.grobid-xml"},"referenced_works_count":85,"referenced_works":["https://openalex.org/W117406676","https://openalex.org/W176204069","https://openalex.org/W230726820","https://openalex.org/W1485490327","https://openalex.org/W1512824425","https://openalex.org/W1523914522","https://openalex.org/W1523918473","https://openalex.org/W1530572757","https://openalex.org/W1571037334","https://openalex.org/W1572299788","https://openalex.org/W1578417629","https://openalex.org/W1592346261","https://openalex.org/W1968570655","https://openalex.org/W1979848457","https://openalex.org/W1982055477","https://openalex.org/W1985289891","https://openalex.org/W1985526537","https://openalex.org/W1995977886","https://openalex.org/W1998167411","https://openalex.org/W2010832227","https://openalex.org/W2011798344","https://openalex.org/W2012833704","https://openalex.org/W2023404461","https://openalex.org/W2026965725","https://openalex.org/W2037337573","https://openalex.org/W2038276547","https://openalex.org/W2038921147","https://openalex.org/W2040088116","https://openalex.org/W2040847787","https://openalex.org/W2043644459","https://openalex.org/W2045533739","https://openalex.org/W2046042060","https://openalex.org/W2049600041","https://openalex.org/W2050749090","https://openalex.org/W2052449446","https://openalex.org/W2053182026","https://openalex.org/W2054081892","https://openalex.org/W2076705731","https://openalex.org/W2084921767","https://openalex.org/W2088101210","https://openalex.org/W2088263428","https://openalex.org/W2088658556","https://openalex.org/W2089706081","https://openalex.org/W2091399525","https://openalex.org/W2107881198","https://openalex.org/W2107917944","https://openalex.org/W2111405401","https://openalex.org/W2114203129","https://openalex.org/W2119338820","https://openalex.org/W2122058331","https://openalex.org/W2129719258","https://openalex.org/W2131709403","https://openalex.org/W2132069633","https://openalex.org/W2137416782","https://openalex.org/W2141793995","https://openalex.org/W2142224482","https://openalex.org/W2146101030","https://openalex.org/W2147717514","https://openalex.org/W2152565070","https://openalex.org/W2157920764","https://openalex.org/W2157988812","https://openalex.org/W2160119100","https://openalex.org/W2160681854","https://openalex.org/W2162663580","https://openalex.org/W2166536886","https://openalex.org/W2167816765","https://openalex.org/W2169838205","https://openalex.org/W2170168647","https://openalex.org/W2320533836","https://openalex.org/W2327230547","https://openalex.org/W2395489635","https://openalex.org/W2405220055","https://openalex.org/W2751862591","https://openalex.org/W2765017642","https://openalex.org/W2950011701","https://openalex.org/W2979473749","https://openalex.org/W3112410551","https://openalex.org/W4230889046","https://openalex.org/W4238411931","https://openalex.org/W4248270945","https://openalex.org/W4256319852","https://openalex.org/W6631282669","https://openalex.org/W6663799693","https://openalex.org/W6679663036","https://openalex.org/W6681625143"],"related_works":["https://openalex.org/W2962922559","https://openalex.org/W2336136902","https://openalex.org/W2598521301","https://openalex.org/W2581021621","https://openalex.org/W2611102007","https://openalex.org/W2182187063","https://openalex.org/W2950149619","https://openalex.org/W2152261259","https://openalex.org/W3123359146","https://openalex.org/W1157599850","https://openalex.org/W3099772093","https://openalex.org/W2493195292","https://openalex.org/W1883031669","https://openalex.org/W2899415272","https://openalex.org/W2796194888","https://openalex.org/W2290541720","https://openalex.org/W2335028541","https://openalex.org/W2522682047","https://openalex.org/W27926580","https://openalex.org/W2767077668"],"abstract_inverted_index":{"An":[0],"outstanding":[1],"open":[2,216],"question":[3,217],"(http://sublinear.info,":[4,218],"Question":[5,219],"#5)":[6],"asks":[7],"to":[8,79,146],"characterize":[9],"metric":[10,50],"spaces":[11,204],"in":[12,103],"which":[13],"distances":[14],"can":[15],"be":[16],"estimated":[17],"using":[18,35],"efficient":[19,29,63,81,117,142,208],"sketches.":[20],"Specifically,":[21],"we":[22,109,199],"say":[23],"that":[24,48,51,111,134,137,202],"a":[25,49,53,112],"sketching":[26,64,102,143],"algorithm":[27],"is":[28,67,72,144],"if":[30,119,122],"it":[31,123],"achieves":[32],"constant":[33,36,129,151],"approximation":[34],"sketch":[37],"size.":[38],"A":[39],"well-known":[40],"result":[41],"of":[42,92,101,105,154],"Indyk":[43],"(J.":[44],"ACM,":[45],"2006)":[46],"implies":[47],"admits":[52,61],"constant-distortion":[54],"embedding":[55,73,147],"into":[56,74,126,148],"lp":[57,75],"for":[58,87,135,184],"p\u2208(0,2]":[59],"also":[60],"an":[62,97],"scheme.":[65],"But":[66],"the":[68,76,88,158,170,177],"converse":[69],"true,":[70],"i.e.,":[71],"only":[77,121],"way":[78],"achieve":[80],"sketching?":[82],"We":[83,131],"address":[84],"these":[85,185,203],"questions":[86],"important":[89],"special":[90],"case":[91],"normed":[93,114],"spaces,":[94],"by":[95,187,194],"providing":[96],"almost":[98],"complete":[99],"characterization":[100],"terms":[104],"embeddings.":[106],"In":[107],"particular,":[108],"prove":[110,133],"finite-dimensional":[113],"space":[115],"allows":[116],"sketches":[118,209],"and":[120,169,189,193],"embeds":[124],"(linearly)":[125],"l1-\u03b5":[127],"with":[128,150],"distortion.":[130,152],"further":[132],"norms":[136,156,186],"are":[138],"closed":[139],"under":[140],"sum-product,":[141],"equivalent":[145],"l1":[149],"Examples":[153],"such":[155],"include":[157],"Earth":[159],"Mover's":[160],"Distance":[161],"(specifically":[162],"its":[163],"norm":[164,172],"variant,":[165],"called":[166],"Kantorovich-Rubinstein":[167],"norm),":[168],"trace":[171],"(a.k.a.":[173],"Schatten":[174],"1-norm":[175],"or":[176],"nuclear":[178],"norm).":[179],"Using":[180],"known":[181],"non-embeddability":[182],"theorems":[183],"Naor":[188],"Schechtman":[190],"(SICOMP,":[191],"2007)":[192],"Pisier":[195],"(Compositio.":[196],"Math.,":[197],"1978),":[198],"then":[200],"conclude":[201],"do":[205],"not":[206],"admit":[207],"either,":[210],"making":[211],"progress":[212],"towards":[213],"answering":[214],"another":[215],"#7).":[220]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
