{"id":"https://openalex.org/W4221056862","doi":"https://doi.org/10.1137/20m1317906","title":"Truly Optimal Euclidean Spanners","display_name":"Truly Optimal Euclidean Spanners","publication_year":2022,"publication_date":"2022-03-31","ids":{"openalex":"https://openalex.org/W4221056862","doi":"https://doi.org/10.1137/20m1317906"},"language":"en","primary_location":{"id":"doi:10.1137/20m1317906","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1317906","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/A5050273950","display_name":"Hung Le","orcid":"https://orcid.org/0000-0001-8223-9944"},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hung Le","raw_affiliation_strings":["University of Massachusetts Amherst, Amherst, MA USA","University of Victoria and University of Massachusetts Amherst"],"affiliations":[{"raw_affiliation_string":"University of Massachusetts Amherst, Amherst, MA USA","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"University of Victoria and University of Massachusetts Amherst","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084685735","display_name":"Shay Solomon","orcid":"https://orcid.org/0000-0003-2254-5100"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shay Solomon","raw_affiliation_strings":["Computer Science and Applied Mathematics, Tel Aviv University, Rehovot, Israel, 76100","Tel Aviv University"],"affiliations":[{"raw_affiliation_string":"Computer Science and Applied Mathematics, Tel Aviv University, Rehovot, Israel, 76100","institution_ids":[]},{"raw_affiliation_string":"Tel Aviv University","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050273950"],"corresponding_institution_ids":["https://openalex.org/I24603500"],"apc_list":null,"apc_paid":null,"fwci":2.5705,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.92741354,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"54","issue":"4","first_page":"FOCS19","last_page":"135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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":0.9998999834060669,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9932000041007996,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9904999732971191,"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/spanner","display_name":"Spanner","score":0.9177184104919434},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7834898233413696},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7228085398674011},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6822316646575928},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.6446428894996643},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6236754655838013},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6074500679969788},{"id":"https://openalex.org/keywords/greedy-algorithm","display_name":"Greedy algorithm","score":0.4988255500793457},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4668273329734802},{"id":"https://openalex.org/keywords/lightness","display_name":"Lightness","score":0.43658214807510376},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32117342948913574},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.185863196849823},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1309182345867157},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11405614018440247}],"concepts":[{"id":"https://openalex.org/C2779585601","wikidata":"https://www.wikidata.org/wiki/Q4049850","display_name":"Spanner","level":2,"score":0.9177184104919434},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7834898233413696},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7228085398674011},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6822316646575928},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6446428894996643},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6236754655838013},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6074500679969788},{"id":"https://openalex.org/C51823790","wikidata":"https://www.wikidata.org/wiki/Q504353","display_name":"Greedy algorithm","level":2,"score":0.4988255500793457},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4668273329734802},{"id":"https://openalex.org/C193601281","wikidata":"https://www.wikidata.org/wiki/Q19426","display_name":"Lightness","level":2,"score":0.43658214807510376},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32117342948913574},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.185863196849823},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1309182345867157},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11405614018440247},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/20m1317906","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1317906","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":[],"awards":[{"id":"https://openalex.org/G5282860457","display_name":null,"funder_award_id":"CCF-2121952","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6968301837","display_name":null,"funder_award_id":"1991/1","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1505970908","https://openalex.org/W1566486010","https://openalex.org/W1769399376","https://openalex.org/W1976125024","https://openalex.org/W1991530421","https://openalex.org/W1997570556","https://openalex.org/W1999658629","https://openalex.org/W2002041206","https://openalex.org/W2004476837","https://openalex.org/W2011958538","https://openalex.org/W2018128607","https://openalex.org/W2020284736","https://openalex.org/W2031671531","https://openalex.org/W2036114412","https://openalex.org/W2041167985","https://openalex.org/W2044180609","https://openalex.org/W2052373622","https://openalex.org/W2062334797","https://openalex.org/W2074149381","https://openalex.org/W2082635360","https://openalex.org/W2086709935","https://openalex.org/W2091915792","https://openalex.org/W2093521781","https://openalex.org/W2107046847","https://openalex.org/W2113604744","https://openalex.org/W2127248062","https://openalex.org/W2131648596","https://openalex.org/W2139391136","https://openalex.org/W2145057516","https://openalex.org/W2160816205","https://openalex.org/W2161408306","https://openalex.org/W2167366051","https://openalex.org/W2264984242","https://openalex.org/W2321124713","https://openalex.org/W2762112321","https://openalex.org/W2774521735","https://openalex.org/W2949684529","https://openalex.org/W2953246643","https://openalex.org/W2963821675","https://openalex.org/W3015517257","https://openalex.org/W3137290582","https://openalex.org/W4214727322","https://openalex.org/W4229802563","https://openalex.org/W4252849733"],"related_works":["https://openalex.org/W3183948672","https://openalex.org/W3173606202","https://openalex.org/W2948807893","https://openalex.org/W2778153218","https://openalex.org/W1969798922","https://openalex.org/W2593488756","https://openalex.org/W2759052040","https://openalex.org/W4290763271","https://openalex.org/W2774521735","https://openalex.org/W2105228010"],"abstract_inverted_index":{"Euclidean":[0,31,83],"spanners":[1,84,137,279,343,369],"are":[2,119,138,258,289],"important":[3],"geometric":[4],"structures,":[5],"having":[6],"found":[7],"numerous":[8],"applications":[9],"over":[10],"the":[11,19,48,95,111,132,141,165,175,200,204,230,239,275,281,305,309,312,340,358,365],"years.":[12],"Cornerstone":[13],"results":[14],"in":[15,79,103,121,146,162,261,292,357,370],"this":[16,217],"area":[17],"from":[18,315],"late":[20],"1980s":[21],"and":[22,42,59,105,113,129,134,151,185,234,236,302,323],"early":[23],"1990s":[24],"state":[25],"that":[26,118,174,238,256,274,287],"for":[27,61,71,178,192,246,263,294,339,364],"any":[28,80,188,247,265,296],"$d$-dimensional":[29],"$n$-point":[30,259,290],"space,":[32],"there":[33,257,288],"exists":[34],"a":[35,88,147,196,329,345,354,378],"$(1+\\epsilon)$-spanner":[36,266,297],"with":[37,344],"$n":[38,126,269],"\\cdot":[39,127,270],"O(\\epsilon^{-d+1})$":[40,128],"edges":[41],"lightness":[43,114,135,300,310,321],"(normalized":[44],"weight)":[45],"$O(\\epsilon^{-2d})$.":[46],"Surprisingly,":[47],"fundamental":[49],"question":[50,76,201],"of":[51,82,136,202,216,311,342,360,367],"whether":[52,203],"or":[53],"not":[54],"these":[55,224],"dependencies":[56,231],"on":[57,131,232,308],"$\\epsilon$":[58,91,99,233],"$d$":[60,63,180,235],"small":[62],"can":[64],"be":[65],"improved":[66],"has":[67],"remained":[68,210],"elusive,":[69],"even":[70],"$d":[72],"=":[73,251],"2$.":[74],"This":[75],"naturally":[77],"arises":[78],"application":[81],"where":[85],"precision":[86],"is":[87,92,100,168,181,207,219,242,372],"necessity":[89],"(thus":[90],"tiny).":[93],"In":[94,144],"most":[96],"extreme":[97],"case":[98],"inverse":[101],"polynomial":[102,120],"$n$,":[104],"then":[106,303,334],"one":[107],"could":[108],"potentially":[109],"improve":[110,304],"size":[112,133,341,359,366],"bounds":[115,125,325],"by":[116,140,195,227],"factors":[117],"$n$.":[122],"The":[123,214],"state-of-the-art":[124],"$O(\\epsilon^{-2d})$":[130,316],"realized":[139],"greedy":[142,166,176,205,240,276,313],"spanner.":[143],"2016,":[145],"preliminary":[148],"version,":[149],"Filtser":[150],"Solomon":[152],"[SIAM":[153],"J.":[154],"Comput.,":[155],"49":[156],"(2020),":[157],"pp.":[158],"429--447]":[159],"proved":[160],"that,":[161],"low-dimensional":[163],"spaces,":[164],"spanner":[167,177,190,206,241,314],"\u201cnear-optimal'';":[169],"informally,":[170],"their":[171],"result":[172,338],"states":[173],"dimension":[179,193],"just":[182],"as":[183,187,374],"sparse":[184],"light":[186],"other":[189],"but":[191],"larger":[194],"constant":[197],"factor.":[198],"Hence":[199],"truly":[208,243],"optimal":[209,282],"open":[211],"to":[212,317,328,353,377],"date.":[213],"contribution":[215],"paper":[218],"twofold:":[220],"(1)":[221],"We":[222,333],"resolve":[223],"longstanding":[225],"questions":[226],"nailing":[228],"down":[229],"showing":[237],"optimal.":[244],"Specifically,":[245],"$d=":[248],"O(1),":[249],"\\epsilon":[250],"\\Omega({n}^{-\\frac{1}{d-1}})$,":[252],"(a)":[253],"we":[254,285],"show":[255,286],"sets":[260,291],"$\\mathbb{R}^d$":[262,293],"which":[264,295],"must":[267,298],"have":[268,299],"\\Omega(\\epsilon^{-d+1})$":[271],"edges,":[272],"implying":[273],"(and":[277],"other)":[278],"achieve":[280],"size;":[283],"(b)":[284],"$\\Omega(\\epsilon^{-d})$,":[301],"upper":[306,322],"bound":[307,363],"$O(\\epsilon^{-d}":[318],"\\log(\\epsilon^{-1}))$.":[319],"(The":[320],"lower":[324],"match":[326],"up":[327],"lower-order":[330,379],"term.)":[331],"(2)":[332],"complement":[335],"our":[336],"negative":[337],"rather":[346],"counterintuitive":[347],"positive":[348],"result:":[349],"Steiner":[350,368],"points":[351],"lead":[352],"quadratic":[355],"improvement":[356],"spanners!":[361],"Our":[362],"$\\mathbb{R}^2$":[371],"tight":[373],"well":[375],"(up":[376],"term).":[380]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
