{"id":"https://openalex.org/W2010820875","doi":"https://doi.org/10.1145/2746539.2746595","title":"A Directed Isoperimetric Inequality with application to Bregman Near Neighbor Lower Bounds","display_name":"A Directed Isoperimetric Inequality with application to Bregman Near Neighbor Lower Bounds","publication_year":2015,"publication_date":"2015-06-03","ids":{"openalex":"https://openalex.org/W2010820875","doi":"https://doi.org/10.1145/2746539.2746595","mag":"2010820875"},"language":"en","primary_location":{"id":"doi:10.1145/2746539.2746595","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2746539.2746595","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"},"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/A5065974640","display_name":"Amirali Abdullah","orcid":null},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Amirali Abdullah","raw_affiliation_strings":["University of Utah, Salt Lake City, UT, USA","University of Utah, Salt Lake City, UT, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Utah, Salt Lake City, UT, USA","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"University of Utah, Salt Lake City, UT, USA#TAB#","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061790878","display_name":"Suresh Venkatasubramanian","orcid":"https://orcid.org/0000-0001-7679-7130"},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Suresh Venkatasubramanian","raw_affiliation_strings":["University of Utah, Salt Lake City, UT, USA","University of Utah, Salt Lake City, UT, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Utah, Salt Lake City, UT, USA","institution_ids":["https://openalex.org/I223532165"]},{"raw_affiliation_string":"University of Utah, Salt Lake City, UT, USA#TAB#","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065974640"],"corresponding_institution_ids":["https://openalex.org/I223532165"],"apc_list":null,"apc_paid":null,"fwci":2.6803,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.88580554,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"509","last_page":"518"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9787999987602234,"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":0.9787999987602234,"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/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9763000011444092,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10057","display_name":"Face and Expression Recognition","score":0.9282000064849854,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/isoperimetric-inequality","display_name":"Isoperimetric inequality","score":0.7962245345115662},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.7536550760269165},{"id":"https://openalex.org/keywords/locality-sensitive-hashing","display_name":"Locality-sensitive hashing","score":0.6652395725250244},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.6036965847015381},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.554801881313324},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5003111362457275},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4919697940349579},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47408783435821533},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4705802798271179},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.434823602437973},{"id":"https://openalex.org/keywords/triangle-inequality","display_name":"Triangle inequality","score":0.4253278374671936},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3804970383644104},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.328940212726593},{"id":"https://openalex.org/keywords/hash-function","display_name":"Hash function","score":0.3276834487915039},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.20201992988586426},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16000550985336304}],"concepts":[{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.7962245345115662},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.7536550760269165},{"id":"https://openalex.org/C74270461","wikidata":"https://www.wikidata.org/wiki/Q1625299","display_name":"Locality-sensitive hashing","level":4,"score":0.6652395725250244},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6036965847015381},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.554801881313324},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5003111362457275},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4919697940349579},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47408783435821533},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4705802798271179},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.434823602437973},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.4253278374671936},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3804970383644104},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.328940212726593},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.3276834487915039},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.20201992988586426},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16000550985336304},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C67388219","wikidata":"https://www.wikidata.org/wiki/Q207440","display_name":"Hash table","level":3,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2746539.2746595","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2746539.2746595","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4300000071525574}],"awards":[],"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":34,"referenced_works":["https://openalex.org/W139808434","https://openalex.org/W1543800554","https://openalex.org/W1546961578","https://openalex.org/W1561129100","https://openalex.org/W1573082642","https://openalex.org/W1593966940","https://openalex.org/W1846376331","https://openalex.org/W1891181203","https://openalex.org/W1985289891","https://openalex.org/W1986296546","https://openalex.org/W1989664320","https://openalex.org/W2002359780","https://openalex.org/W2033468335","https://openalex.org/W2037046390","https://openalex.org/W2045745231","https://openalex.org/W2053267965","https://openalex.org/W2062539466","https://openalex.org/W2075057405","https://openalex.org/W2077810240","https://openalex.org/W2080479164","https://openalex.org/W2080995342","https://openalex.org/W2081256580","https://openalex.org/W2095681182","https://openalex.org/W2096765209","https://openalex.org/W2098375959","https://openalex.org/W2116327295","https://openalex.org/W2134146845","https://openalex.org/W2155074354","https://openalex.org/W2160709761","https://openalex.org/W2399996194","https://openalex.org/W2620598837","https://openalex.org/W2949466244","https://openalex.org/W2949874440","https://openalex.org/W2963834565"],"related_works":["https://openalex.org/W2393012656","https://openalex.org/W4293733602","https://openalex.org/W2000601968","https://openalex.org/W2144265691","https://openalex.org/W2033383639","https://openalex.org/W3108918257","https://openalex.org/W183456729","https://openalex.org/W3016124764","https://openalex.org/W2105470228","https://openalex.org/W2107485210"],"abstract_inverted_index":{"Bregman":[0,131],"divergences":[1],"are":[2,7,21],"important":[3],"distance":[4],"measures":[5],"that":[6,77,114,135,152],"used":[8],"in":[9,26],"applications":[10],"such":[11],"as":[12],"computer":[13],"vision,":[14],"text":[15],"mining,":[16],"and":[17,20,43,65,86],"speech":[18],"processing,":[19],"a":[22,71,81,101],"focus":[23,123],"of":[24,39,127],"interest":[25],"machine":[27],"learning":[28],"due":[29],"to":[30,49,99],"their":[31],"information-theoretic":[32],"properties.":[33],"There":[34],"has":[35],"been":[36],"extensive":[37],"study":[38],"algorithms":[40],"for":[41,130,148,165],"clustering":[42],"near":[44],"neighbor":[45],"search":[46,129,151],"with":[47],"respect":[48],"these":[50],"divergences.":[51,132],"In":[52,92,106,163],"all":[53],"cases,":[54],"the":[55,61,97,111,125,137,169],"guarantees":[56],"depend":[57],"not":[58],"just":[59],"on":[60,70,80,117,124],"data":[62,143],"size":[63],"n":[64],"dimensionality":[66],"d,":[67],"but":[68],"also":[69],"structure":[72,144],"constant":[73],"\u03bc":[74,95,118],"\u2265":[75],"1":[76],"depends":[78],"solely":[79],"generating":[82],"convex":[83],"function":[84],"\u03c6":[85],"can":[87],"grow":[88],"without":[89],"bound":[90,171],"independently.":[91],"general,":[93],"this":[94,107,115],"parametrizes":[96],"degree":[98],"which":[100],"given":[102],"divergence":[103],"is":[104,172],"\"asymmetric\".":[105],"paper,":[108],"we":[109],"provide":[110],"first":[112],"evidence":[113],"dependence":[116],"might":[119],"be":[120],"intrinsic.":[121],"We":[122,133],"problem":[126],"ac{ann}":[128],"show":[134],"under":[136,167],"cell":[138],"probe":[139],"model,":[140],"any":[141],"non-adaptive":[142],"(like":[145],"locality-sensitive":[146],"hashing)":[147],"c-approximate":[149],"near-neighbor":[150],"admits":[153],"r":[154],"probes":[155],"must":[156],"use":[157],"space":[158],"\u03a9(dn1":[159],"+":[160],"\u03bc/c":[161],"r).":[162],"contrast":[164],"LSH":[166],"l1":[168],"best":[170],"\u03a9(dn1+":[173],"1/cr).":[174]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}