{"id":"https://openalex.org/W3137290582","doi":"https://doi.org/10.1145/2915183","title":"On Hierarchical Routing in Doubling Metrics","display_name":"On Hierarchical Routing in Doubling Metrics","publication_year":2016,"publication_date":"2016-08-16","ids":{"openalex":"https://openalex.org/W3137290582","doi":"https://doi.org/10.1145/2915183","mag":"3137290582"},"language":"en","primary_location":{"id":"doi:10.1145/2915183","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2915183","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2915183&type=pdf","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","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://dl.acm.org/ft_gateway.cfm?id=2915183&type=pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018708584","display_name":"T-H. Hubert Chan","orcid":"https://orcid.org/0000-0002-8340-235X"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"T.-H. Hubert Chan","raw_affiliation_strings":["The University of Hong Kong, Pokfulam Road, Hong Kong"],"affiliations":[{"raw_affiliation_string":"The University of Hong Kong, Pokfulam Road, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078381067","display_name":"Anupam Gupta","orcid":"https://orcid.org/0000-0001-5579-3405"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anupam Gupta","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh PA, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046808993","display_name":"Bruce M. Maggs","orcid":"https://orcid.org/0000-0002-5692-7062"},"institutions":[{"id":"https://openalex.org/I10734018","display_name":"Akamai (United States)","ror":"https://ror.org/03tarb191","country_code":"US","type":"company","lineage":["https://openalex.org/I10734018"]},{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bruce M. Maggs","raw_affiliation_strings":["Duke University and Akamai Technologies, NC, USA"],"affiliations":[{"raw_affiliation_string":"Duke University and Akamai Technologies, NC, USA","institution_ids":["https://openalex.org/I10734018","https://openalex.org/I170897317"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102323261","display_name":"Shuheng Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shuheng Zhou","raw_affiliation_strings":["University of Michigan, MI, USA"],"affiliations":[{"raw_affiliation_string":"University of Michigan, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018708584"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":2.8753,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.91900293,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"12","issue":"4","first_page":"1","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9891999959945679,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9891999959945679,"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":0.9883000254631042,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9689000248908997,"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/mathematics","display_name":"Mathematics","score":0.6854088306427002},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6700212955474854},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6157656908035278},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4754640460014343},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4296368956565857},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.37583398818969727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6854088306427002},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6700212955474854},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6157656908035278},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4754640460014343},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4296368956565857},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.37583398818969727}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1145/2915183","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2915183","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2915183&type=pdf","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:figshare.com:article/6607850","is_oa":true,"landing_page_url":null,"pdf_url":"https://figshare.com/articles/On_Hierarchical_Routing_in_Doubling_Metrics/6607850","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:repository.cmu.edu:compsci-1841","is_oa":false,"landing_page_url":"http://repository.cmu.edu/cgi/viewcontent.cgi?article=1841&context=compsci","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"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","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.649.5550","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.649.5550","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.919.3406","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.919.3406","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://repository.cmu.edu/cgi/viewcontent.cgi?article%3D1841%26context%3Dcompsci","raw_type":"text"},{"id":"pmh:oai:hub.hku.hk:10722/232838","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/232838","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.1184/r1/6607850.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6607850.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1145/2915183","is_oa":true,"landing_page_url":"https://doi.org/10.1145/2915183","pdf_url":"http://dl.acm.org/ft_gateway.cfm?id=2915183&type=pdf","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":[],"awards":[{"id":"https://openalex.org/G1791435978","display_name":null,"funder_award_id":"CNF 0435382, CNF 0433540, ANI 0331653, CCR 0205523","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2345276091","display_name":"Information Technology Research (ITR):  ITR/ANIR 100 MB/SEC for 100 Million Households","funder_award_id":"0331653","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G391991289","display_name":null,"funder_award_id":"433540","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5117965193","display_name":"NeTS-NR:     A Measurement-Driven Approach to Internet Protocol and Systems Design","funder_award_id":"0435382","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5284393966","display_name":"ITR:    Scalable Molecular Electronics","funder_award_id":"0205523","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5478771362","display_name":"CyberTrust Center:  Security Through Interaction Modeling (STIM)","funder_award_id":"0433540","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5653896175","display_name":null,"funder_award_id":"DAAD19-02-1-0389","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8094226035","display_name":null,"funder_award_id":"DAAD19-02-1-0389, DAAD19 02 1 0389","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3137290582.pdf","grobid_xml":"https://content.openalex.org/works/W3137290582.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W1523004878","https://openalex.org/W1727575636","https://openalex.org/W1769399376","https://openalex.org/W1974130741","https://openalex.org/W1994772769","https://openalex.org/W1997027778","https://openalex.org/W2000876023","https://openalex.org/W2005580106","https://openalex.org/W2006383304","https://openalex.org/W2007575140","https://openalex.org/W2011571064","https://openalex.org/W2014411916","https://openalex.org/W2019731444","https://openalex.org/W2022392080","https://openalex.org/W2034188144","https://openalex.org/W2039498863","https://openalex.org/W2053578961","https://openalex.org/W2055362092","https://openalex.org/W2055488252","https://openalex.org/W2062334797","https://openalex.org/W2063048655","https://openalex.org/W2067259587","https://openalex.org/W2068871408","https://openalex.org/W2074149381","https://openalex.org/W2077824753","https://openalex.org/W2079609983","https://openalex.org/W2091569826","https://openalex.org/W2093521781","https://openalex.org/W2102465486","https://openalex.org/W2107046847","https://openalex.org/W2109693504","https://openalex.org/W2114493937","https://openalex.org/W2127248062","https://openalex.org/W2133065816","https://openalex.org/W2140279174","https://openalex.org/W2154201790","https://openalex.org/W2154833764","https://openalex.org/W2158907148","https://openalex.org/W2160277501","https://openalex.org/W2165222121","https://openalex.org/W2169036209","https://openalex.org/W2293001982","https://openalex.org/W2620916615","https://openalex.org/W4389615669"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W2002282073","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W2790190308","https://openalex.org/W4301046126"],"abstract_inverted_index":{"We":[0,38,81,98,188],"study":[1],"the":[2,83,88,144,147,152,156,161,203,239],"problem":[3],"of":[4,31,65,121,146,155,163,185,193,241],"routing":[5,15,24,32,106,119,164,204],"in":[6,16,91],"doubling":[7,49,70,75,176,197],"metrics":[8,18,198],"and":[9,22,149,181],"show":[10,99],"how":[11,100],"to":[12,101,214],"perform":[13,102],"hierarchical":[14],"such":[17,108],"with":[19,27,118,132,228],"small":[20,29],"stretch":[21],"compact":[23],"tables":[25,120,205],"(i.e.,":[26],"a":[28,41,79,109,221],"amount":[30],"information":[33],"stored":[34],"at":[35,52,123,231],"each":[36],"vertex).":[37],"say":[39],"that":[40],"metric":[42,71,84,110,222],"(":[43,223],"X":[44,224],",":[45,140,225,237],"d":[46,226],")":[47,227],"has":[48],"dimension":[50,76],"dim(<i<X</i<)":[51,77],"most":[53,124,232],"\u03b1":[54,63],"if":[55],"every":[56],"ball":[57],"can":[58],"be":[59],"covered":[60],"by":[61,87],"2":[62],"balls":[64],"half":[66],"its":[67],"radius.":[68],"(A":[69],"is":[72,78,143,151,167],"one":[73],"whose":[74],"constant.)":[80],"consider":[82],"space":[85],"induced":[86],"shortest-path":[89],"distance":[90],"an":[92],"underlying":[93],"undirected":[94],"graph":[95,157],"G":[96,158],".":[97],"(1":[103,216],"+":[104,217,234],"\u03c4)-stretch":[105,218],"on":[107,183],"for":[111,175,196,207,220,245],"any":[112],"0":[113],"<":[114],"\u03c4":[115,169,208],"\u2264":[116],"1":[117],"size":[122],"(\u03b1/\u03c4)":[125,134],"O":[126,135,171],"(\u03b1)":[127,136],"log":[128,137,173],"\u0394log":[129],"\u03b4":[130,150],"bits":[131],"only":[133],"\u0394":[138,142,174],"entries":[139,166],"where":[141],"diameter":[145],"graph,":[148],"maximum":[153,229],"degree":[154,230],";":[159],"hence,":[160],"number":[162],"table":[165],"just":[168],"\u2212":[170],"(1)":[172],"metrics.":[177,247],"These":[178],"results":[179,240],"extend":[180],"improve":[182],"those":[184,200],"Talwar":[186],"(2004).":[187],"also":[189],"give":[190,212],"better":[191],"constructions":[192],"sparse":[194],"spanners":[195,219],"than":[199],"obtained":[201],"from":[202],"earlier;":[206],">":[209],"0,":[210],"we":[211],"algorithms":[213],"construct":[215],"(2":[233],"1/\u03c4)":[235],"O(dim(X))":[236],"matching":[238],"Das":[242],"et":[243],"al.":[244],"Euclidean":[246]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}