{"id":"https://openalex.org/W865313152","doi":"https://doi.org/10.1137/140977655","title":"On the Impossibility of Dimension Reduction for Doubling Subsets of $\\ell_{p}$","display_name":"On the Impossibility of Dimension Reduction for Doubling Subsets of $\\ell_{p}$","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W865313152","doi":"https://doi.org/10.1137/140977655","mag":"865313152"},"language":"en","primary_location":{"id":"doi:10.1137/140977655","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140977655","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","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/A5111723795","display_name":"Yair Bartal","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yair Bartal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057494907","display_name":"Lee-Ad Gottlieb","orcid":"https://orcid.org/0000-0003-3355-351X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee-Ad Gottlieb","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066182501","display_name":"Ofer Neiman","orcid":"https://orcid.org/0000-0003-4179-4364"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ofer Neiman","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":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.00993433,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":"3","first_page":"1207","last_page":"1222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9821000099182129,"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/T11591","display_name":"NF-\u03baB Signaling Pathways","score":0.9453999996185303,"subfield":{"id":"https://openalex.org/subfields/1306","display_name":"Cancer Research"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8560887575149536},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7733489274978638},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6561573147773743},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6115843057632446},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.596524715423584},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5772672891616821},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5174737572669983},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.500777006149292},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.49926018714904785},{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.466718852519989},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.46173322200775146},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.4241219758987427},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4032549560070038},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08637195825576782},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07959401607513428}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8560887575149536},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7733489274978638},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6561573147773743},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6115843057632446},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.596524715423584},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5772672891616821},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5174737572669983},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.500777006149292},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.49926018714904785},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.466718852519989},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.46173322200775146},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.4241219758987427},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4032549560070038},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08637195825576782},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07959401607513428},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","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},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.0},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140977655","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140977655","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W48861618","https://openalex.org/W1594954118","https://openalex.org/W1987836603","https://openalex.org/W2030449718","https://openalex.org/W2036959865","https://openalex.org/W2045533739","https://openalex.org/W2045745231","https://openalex.org/W2075022748","https://openalex.org/W2076081748","https://openalex.org/W2083854723","https://openalex.org/W2091170478","https://openalex.org/W2093480133","https://openalex.org/W2095439633","https://openalex.org/W2103164654","https://openalex.org/W2149463264","https://openalex.org/W2176446742","https://openalex.org/W2208163925","https://openalex.org/W2583644876","https://openalex.org/W2621446776","https://openalex.org/W2788840627","https://openalex.org/W2949396230","https://openalex.org/W2962980142","https://openalex.org/W2963683232","https://openalex.org/W3098011928","https://openalex.org/W3103354817"],"related_works":["https://openalex.org/W2384156839","https://openalex.org/W4321602641","https://openalex.org/W2394251275","https://openalex.org/W915072206","https://openalex.org/W4241392912","https://openalex.org/W2489497330","https://openalex.org/W2596801716","https://openalex.org/W4387391601","https://openalex.org/W2299263302","https://openalex.org/W2021362375"],"abstract_inverted_index":{"A":[0],"major":[1],"open":[2],"problem":[3],"in":[4],"the":[5,11,31,35,74],"field":[6],"of":[7,13,19,34,62,73],"metric":[8],"embedding":[9,72],"is":[10],"existence":[12],"dimension":[14,27],"reduction":[15],"for":[16,50],"$n$-point":[17,60],"subsets":[18],"Euclidean":[20],"space,":[21],"such":[22],"that":[23,70],"both":[24],"distortion":[25,79],"and":[26,38,68],"depend":[28],"only":[29],"on":[30,40],"doubling":[32,65],"constant":[33,66],"point":[36],"set,":[37],"not":[39],"its":[41],"cardinality.":[42],"In":[43,55],"this":[44,48],"paper,":[45],"we":[46,57],"negate":[47],"possibility":[49],"$\\ell_p$":[51,63],"spaces":[52],"with":[53,64,78],"$p>2$.":[54],"particular,":[56],"introduce":[58],"an":[59],"subset":[61],"$O(1)$,":[67],"demonstrate":[69],"any":[71],"set":[75],"into":[76],"$\\ell_p^d$":[77],"$D$":[80],"must":[81],"have":[82],"$D\\ge\\Omega((\\frac{\\log":[83],"n}{d})^{\\frac{1}{2}-\\frac{1}{p}})$.":[84]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}