{"id":"https://openalex.org/W4362578421","doi":"https://doi.org/10.1145/3590771","title":"Greedy Spanners in Euclidean Spaces Admit Sublinear Separators","display_name":"Greedy Spanners in Euclidean Spaces Admit Sublinear Separators","publication_year":2023,"publication_date":"2023-04-03","ids":{"openalex":"https://openalex.org/W4362578421","doi":"https://doi.org/10.1145/3590771"},"language":"en","primary_location":{"id":"doi:10.1145/3590771","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3590771","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3590771","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3590771","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/I177605424","display_name":"Amherst College","ror":"https://ror.org/028vqfs63","country_code":"US","type":"education","lineage":["https://openalex.org/I177605424"]},{"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":false,"raw_author_name":"Hung Le","raw_affiliation_strings":["University of Massachusetts Amherst, Amherst, USA","University of Massachusetts Amherst, 120 Tillson Farm Road, Amherst, MA, USA, 01003-9346"],"raw_orcid":"https://orcid.org/0000-0001-8223-9944","affiliations":[{"raw_affiliation_string":"University of Massachusetts Amherst, Amherst, USA","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"University of Massachusetts Amherst, 120 Tillson Farm Road, Amherst, MA, USA, 01003-9346","institution_ids":["https://openalex.org/I177605424","https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050147589","display_name":"Cuong Than","orcid":"https://orcid.org/0000-0001-7350-331X"},"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":false,"raw_author_name":"Cuong Than","raw_affiliation_strings":["University of Massachusetts Amherst, Amherst, USA"],"raw_orcid":"https://orcid.org/0000-0001-7350-331X","affiliations":[{"raw_affiliation_string":"University of Massachusetts Amherst, Amherst, USA","institution_ids":["https://openalex.org/I24603500"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0565046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"3","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9995999932289124,"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":0.9995999932289124,"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.991100013256073,"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/sublinear-function","display_name":"Sublinear function","score":0.839573860168457},{"id":"https://openalex.org/keywords/spanner","display_name":"Spanner","score":0.821916401386261},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8176171183586121},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6442065238952637},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5402957797050476},{"id":"https://openalex.org/keywords/separator","display_name":"Separator (oil production)","score":0.4800620973110199},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4650636315345764},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43595266342163086},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37628084421157837},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13345900177955627},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13033434748649597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11885958909988403}],"concepts":[{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.839573860168457},{"id":"https://openalex.org/C2779585601","wikidata":"https://www.wikidata.org/wiki/Q4049850","display_name":"Spanner","level":2,"score":0.821916401386261},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8176171183586121},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6442065238952637},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5402957797050476},{"id":"https://openalex.org/C185004128","wikidata":"https://www.wikidata.org/wiki/Q3011536","display_name":"Separator (oil production)","level":2,"score":0.4800620973110199},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4650636315345764},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43595266342163086},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37628084421157837},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13345900177955627},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13033434748649597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11885958909988403},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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":2,"locations":[{"id":"doi:10.1145/3590771","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3590771","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3590771","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:scholarworks.umass.edu:cs_faculty_pubs-2371","is_oa":false,"landing_page_url":"https://scholarworks.umass.edu/context/cs_faculty_pubs/article/2371/viewcontent/3590771.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306402240","display_name":"ScholarWorks@UMassAmherst (University of Massachusetts Amherst)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I24603500","host_organization_name":"University of Massachusetts Amherst","host_organization_lineage":["https://openalex.org/I24603500"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computer Science Department Faculty Publication Series","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1145/3590771","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3590771","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3590771","source":{"id":"https://openalex.org/S137348503","display_name":"ACM Transactions on Algorithms","issn_l":"1549-6325","issn":["1549-6325","1549-6333"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G3133442982","display_name":"NSF-BSF: Small: AF: Towards a Unified Theory of Spanners","funder_award_id":"2121952","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4362578421.pdf","grobid_xml":"https://content.openalex.org/works/W4362578421.grobid-xml"},"referenced_works_count":64,"referenced_works":["https://openalex.org/W11848909","https://openalex.org/W1505970908","https://openalex.org/W1518500386","https://openalex.org/W1599688444","https://openalex.org/W1603676814","https://openalex.org/W1606162993","https://openalex.org/W1930019869","https://openalex.org/W1956345397","https://openalex.org/W1964111962","https://openalex.org/W1965909513","https://openalex.org/W1976125024","https://openalex.org/W1982180670","https://openalex.org/W1989638756","https://openalex.org/W1991530421","https://openalex.org/W2002041206","https://openalex.org/W2005128841","https://openalex.org/W2007069176","https://openalex.org/W2020284736","https://openalex.org/W2026498642","https://openalex.org/W2038973759","https://openalex.org/W2041167985","https://openalex.org/W2045134120","https://openalex.org/W2059707428","https://openalex.org/W2064525670","https://openalex.org/W2065166038","https://openalex.org/W2067431706","https://openalex.org/W2068019092","https://openalex.org/W2083352539","https://openalex.org/W2093521781","https://openalex.org/W2106718857","https://openalex.org/W2130481157","https://openalex.org/W2131648596","https://openalex.org/W2144668683","https://openalex.org/W2144677702","https://openalex.org/W2145057516","https://openalex.org/W2145145566","https://openalex.org/W2147868672","https://openalex.org/W2154583779","https://openalex.org/W2156760067","https://openalex.org/W2159525520","https://openalex.org/W2264984242","https://openalex.org/W2398255676","https://openalex.org/W2604499455","https://openalex.org/W2729560458","https://openalex.org/W2762935521","https://openalex.org/W2774521735","https://openalex.org/W2795067502","https://openalex.org/W2951040439","https://openalex.org/W2953246643","https://openalex.org/W2962856411","https://openalex.org/W2962961215","https://openalex.org/W2963153697","https://openalex.org/W2963821675","https://openalex.org/W2971434485","https://openalex.org/W3127920245","https://openalex.org/W3135932689","https://openalex.org/W3137290582","https://openalex.org/W3172663538","https://openalex.org/W4205300528","https://openalex.org/W4242151229","https://openalex.org/W4245082111","https://openalex.org/W4285451384","https://openalex.org/W6636233890","https://openalex.org/W6791885766"],"related_works":["https://openalex.org/W4376651360","https://openalex.org/W4297580473","https://openalex.org/W2949656589","https://openalex.org/W2398255676","https://openalex.org/W2026144971","https://openalex.org/W1584948383","https://openalex.org/W4290763271","https://openalex.org/W2774521735","https://openalex.org/W229853467","https://openalex.org/W4294294347"],"abstract_inverted_index":{"The":[0],"greedy":[1,49,69,105,144,235,347,392],"spanner":[2,50,70,106,145,236,348,393],"in":[3,51,58,71,107,146,201,214,260,327,394],"a":[4,9,30,55,59,75,100,150,158,163,172,218,243,281,290,295,315,325,335,360],"low-dimensional":[5],"Euclidean":[6,389],"space":[7,354],"is":[8,84,88,183,237,370,380],"fundamental":[10],"geometric":[11,168,181,209],"construction":[12],"that":[13,47,136,161,175,206,233,247,278,345],"has":[14,74,149,217,359,397],"been":[15],"extensively":[16],"studied":[17],"over":[18],"three":[19],"decades,":[20],"as":[21,116],"it":[22],"possesses":[23],"the":[24,48,68,97,104,125,143,202,234,273,340,346,371,374,376,384,391],"two":[25],"most":[26,193],"basic":[27],"properties":[28],"of":[29,64,67,77,99,127,139,142,152,188,196,211,220,256,286,297,330,349,355,362,373,407],"good":[31],"spanner:":[32],"constant":[33,37,112,291],"maximum":[34,292,399],"degree":[35,293,400],"and":[36,41,87,129,253,294,310],"lightness.":[38],"Recently,":[39],"Eppstein":[40,128],"Khodabandeh":[42,130],"[":[43,131,312],"28":[44,132],"]":[45,133,314],"showed":[46],"\\(\\mathbb":[52,72,108,147,215,261],"{R}^2\\)":[53,73],"admits":[54],"sublinear":[56,173,336],"separator":[57,76,102,151,174,219,296,361],"strong":[60],"sense:":[61],"Any":[62],"subgraph":[63,138],"k":[65,140],"vertices":[66,141,213],"size":[78,153,221,298,363],"\\(O(\\sqrt":[79],"{k})\\)":[80],".":[81,155,224,263,401],"Their":[82],"technique":[83,160,265],"inherently":[85],"planar":[86],"not":[89],"extensible":[90],"to":[91,170,249,268,276,333,343,383],"higher":[92],"dimensions.":[93],"They":[94],"left":[95],"showing":[96,135,232],"existence":[98],"small":[101],"for":[103,110,166,283,324],"{R}^d\\)":[109,148,216,262],"any":[111,137,167,186,207],"d":[113,288,332,358],"\u2265":[114],"3":[115],"an":[117,304,350],"open":[118,305],"problem.":[119],"In":[120],"this":[121,301],"article,":[122],"we":[123,176,403],"resolve":[124],"problem":[126,306],"by":[134,231,308],"\\(O(k^{1-1/d})\\)":[154],"We":[156,204,225,240,271,318,338],"introduce":[157,320],"new":[159,341],"gives":[162],"simple":[164,322],"criterion":[165,275,323,342],"graph":[169,182,210,326],"have":[171,334],"dub":[177],"\u03c4-lanky":[178,184,208,274],":":[179],"A":[180],"if":[185],"ball":[187,251],"radius":[189],"r":[190,200],"cuts":[191],"at":[192,198],"\u03c4":[194],"edges":[195],"length":[197],"least":[199],"graph.":[203],"show":[205,277,344],"n":[212,351],"\\(O(\\tau":[222],"n^{1-1/d})\\)":[223],"then":[226,319],"derive":[227],"our":[228,408],"main":[229],"result":[230,246,302],"O":[238],"(1)-lanky.":[239],"indeed":[241],"obtain":[242],"more":[244],"general":[245],"applies":[248],"unit":[250],"graphs":[252],"point":[254],"sets":[255],"low":[257],"fractal":[258],"dimensions":[259],"Our":[264],"naturally":[266],"extends":[267],"doubling":[269,284,328,356,395],"metrics.":[270],"use":[272,339],"there":[279],"exists":[280],"(1+\u03b5)-spanner":[282],"metrics":[285,329,396],"dimension":[287,331,357],"with":[289],"\\(O(n^{1-\\frac{1}{d}})\\)":[299],";":[300],"resolves":[303],"posed":[307],"Abam":[309],"Har-Peled":[311],"1":[313],"decade":[316],"ago.":[317],"another":[321],"separator.":[337],"-point":[352],"metric":[353],"\\(O((n^{1-\\frac{1}{d}})":[364],"+":[365],"\\log":[366],"\\Delta)\\)":[367],"where":[368],"\u0394":[369],"spread":[372],"metric;":[375],"factor":[377],"log":[378],"(\u0394)":[379],"tightly":[381],"connected":[382],"fact":[385],"that,":[386],"unlike":[387],"its":[388],"counterpart,":[390],"unbounded":[398],"Finally,":[402],"discuss":[404],"algorithmic":[405],"implications":[406],"results.":[409]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}