{"id":"https://openalex.org/W3002374308","doi":"https://doi.org/10.1137/21m1436221","title":"Lossless Prioritized Embeddings","display_name":"Lossless Prioritized Embeddings","publication_year":2022,"publication_date":"2022-07-05","ids":{"openalex":"https://openalex.org/W3002374308","doi":"https://doi.org/10.1137/21m1436221","mag":"3002374308"},"language":"en","primary_location":{"id":"doi:10.1137/21m1436221","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1436221","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/A5075683085","display_name":"Michael Elkin","orcid":"https://orcid.org/0000-0003-4257-2122"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michael Elkin","raw_affiliation_strings":["Ben\u2010Gurion University of the Negev"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ben\u2010Gurion University of the Negev","institution_ids":["https://openalex.org/I124227911"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066182501","display_name":"Ofer Neiman","orcid":"https://orcid.org/0000-0003-4179-4364"},"institutions":[{"id":"https://openalex.org/I124227911","display_name":"Ben-Gurion University of the Negev","ror":"https://ror.org/05tkyf982","country_code":"IL","type":"education","lineage":["https://openalex.org/I124227911"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ofer Neiman","raw_affiliation_strings":["Ben\u2010Gurion University of the Negev"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ben\u2010Gurion University of the Negev","institution_ids":["https://openalex.org/I124227911"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I124227911"],"apc_list":null,"apc_paid":null,"fwci":0.2656,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50848712,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"36","issue":"3","first_page":"1529","last_page":"1550"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9959999918937683,"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":0.9959999918937683,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9674000144004822,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9455000162124634,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7411785125732422},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.6703170537948608},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6679506301879883},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6271287202835083},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6102660894393921},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5663841962814331},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36549806594848633},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1514480710029602},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1313551664352417}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7411785125732422},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.6703170537948608},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6679506301879883},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6271287202835083},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6102660894393921},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5663841962814331},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36549806594848633},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1514480710029602},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1313551664352417},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1436221","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1436221","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":[{"id":"https://openalex.org/G1399582570","display_name":null,"funder_award_id":"(1817/17)","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G6446845382","display_name":null,"funder_award_id":"2344/19","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1489554686","https://openalex.org/W1500591628","https://openalex.org/W1501987263","https://openalex.org/W1905029509","https://openalex.org/W1981859328","https://openalex.org/W2017427469","https://openalex.org/W2018128607","https://openalex.org/W2027697499","https://openalex.org/W2031536548","https://openalex.org/W2041571997","https://openalex.org/W2042333226","https://openalex.org/W2045446569","https://openalex.org/W2063491776","https://openalex.org/W2114493937","https://openalex.org/W2127248062","https://openalex.org/W2167816765","https://openalex.org/W2176446742","https://openalex.org/W2569942321","https://openalex.org/W2571257893","https://openalex.org/W2583644876","https://openalex.org/W2621446776","https://openalex.org/W2750647157","https://openalex.org/W2807887246","https://openalex.org/W2809400127","https://openalex.org/W2900806478","https://openalex.org/W2924819758","https://openalex.org/W2949625395","https://openalex.org/W2959559668","https://openalex.org/W2962691590","https://openalex.org/W2963298223","https://openalex.org/W3001458282","https://openalex.org/W3030774092","https://openalex.org/W4212770610","https://openalex.org/W4245082111","https://openalex.org/W4298334495"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W2183306018","https://openalex.org/W2549990292","https://openalex.org/W2013985456","https://openalex.org/W2951564084","https://openalex.org/W4302984940","https://openalex.org/W2776807270","https://openalex.org/W2392685819","https://openalex.org/W2009836834","https://openalex.org/W2914691919"],"abstract_inverted_index":{"Given":[0],"metric":[1],"spaces":[2],"$(X,d)$":[3],"and":[4,6,85,94,123,212,269,309,351],"$(Y,\\rho)$":[5],"an":[7,12,240],"ordering":[8],"$x_1,x_2,\\ldots,x_n$":[9],"of":[10,35,78,175,179,197,244,257,260,264,285,325,336,344,352],"$(X,d)$,":[11],"embedding":[13,59,80,196,243,263,284],"$f:":[14],"X":[15],"\\rightarrow":[16],"Y$":[17],"is":[18,48,54,60,164,185,191,239,280],"said":[19,61],"to":[20,62,133,172],"have":[21,63,70],"a":[22,27,55,105,167,204,281,292,333,348,356],"prioritized":[23,64,79,138,155,234,242,282,296,342],"distortion":[24,41,162,174,210,297,324],"$\\alpha(\\cdot)$,":[25,29],"for":[26,31,45,109,187,194,203,291],"function":[28],"if":[30,67],"any":[32],"pair":[33,47],"$x_j,x'$":[34],"distinct":[36],"points":[37],"in":[38,89,145,151,221,322],"$X$,":[39],"the":[40,58,86,146,152,173,176,254,261,318,323,326],"provided":[42],"by":[43,83],"$f$":[44],"this":[46,116,159,222,228],"at":[49,71,165],"most":[50,72],"$\\alpha(j)$.":[51],"If":[52],"$Y$":[53],"normed":[56],"space,":[57],"dimension":[65,213,250,310],"$\\beta(\\cdot)$":[66],"$f(x_j)$":[68],"may":[69],"$\\beta(j)$":[73],"nonzero":[74],"coordinates.":[75],"The":[76,236,277],"notion":[77],"was":[81,113],"introduced":[82],"Filtser":[84],"current":[87],"authors":[88],"[M.":[90,119],"Elkin,":[91,120],"A.":[92,121],"Filtser,":[93,122],"O.":[95,124],"Neiman,":[96,125],"SIAM":[97,126],"J.":[98,127],"Comput.,":[99,128],"47":[100,129],"(2018),":[101,130],"pp.":[102,131,275],"829--858],":[103],"where":[104],"rather":[106],"general":[107,198,286,345,353],"methodology":[108,117,160],"constructing":[110],"such":[111],"embeddings":[112,156,343],"developed.":[114],"Though":[115],"enabled":[118],"829--858]":[132],"come":[134],"up":[135],"with":[136,249,360],"many":[137],"embeddings,":[139],"it":[140],"typically":[141],"incurs":[142],"some":[143],"loss":[144,184],"distortion.":[147,363],"In":[148,227],"other":[149],"words,":[150],"worst":[153],"case,":[154],"obtained":[157],"via":[158],"incur":[161],"which":[163],"least":[166],"constant":[168,183],"factor":[169],"off":[170],"compared":[171],"classical":[177,262,327],"counterparts":[178],"these":[180],"embeddings.":[181,189,235],"This":[182],"problematic":[186],"isometric":[188,241],"It":[190],"also":[192,331],"troublesome":[193],"Matou\u0161ek's":[195,337],"metrics":[199,246,287,346],"into":[200,247,288,347,355],"$\\ell_\\infty$,":[201,289],"which,":[202,290],"parameter":[205,293],"$k":[206],"=":[207],"1,2,\\ldots$,":[208],"provides":[209,295],"$2k-1$":[211,321],"$O(k":[214,311],"\\log":[215,312],"n":[216,313],"\\cdot":[217,314],"n^{1/k})$.":[218],"All":[219],"logarithms":[220],"paper":[223,229],"are":[224],"base":[225],"2.":[226],"we":[230,340],"devise":[231,341],"two":[232],"lossless":[233],"first":[237],"one":[238,279],"tree":[245],"$\\ell_\\infty$":[248],"$O(\\log":[251,258],"j)$,":[252],"matching":[253,317],"worst-case":[255,319],"guarantee":[256,320],"n)$":[259],"[N.":[265],"Linial,":[266],"E.":[267],"London,":[268],"Y.":[270],"Rabinovich,":[271],"Combinatorica,":[272],"15":[273],"(1995),":[274],"215--245].":[276],"second":[278],"Matou\u0161ek":[283,328],"$k=1,2,\\ldots$,":[294],"$2":[298],"\\lceil":[299],"k":[300],"{{\\log":[301],"j}":[302],"\\over":[303],"{\\log":[304],"n}}":[305],"\\rceil":[306],"-":[307],"1$":[308],"n^{1/k})$,":[315],"again":[316],"embedding.":[329,338],"We":[330],"provide":[332],"dimension-prioritized":[334],"variant":[335],"Finally,":[339],"single":[349,357],"ultrametric":[350],"graphs":[354],"spanning":[358],"tree,":[359],"asymptotically":[361],"optimal":[362]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
