{"id":"https://openalex.org/W2620725079","doi":"https://doi.org/10.1109/tit.2017.2710184","title":"The Global Packing Number of a Fat-Tree Network","display_name":"The Global Packing Number of a Fat-Tree Network","publication_year":2017,"publication_date":"2017-06-01","ids":{"openalex":"https://openalex.org/W2620725079","doi":"https://doi.org/10.1109/tit.2017.2710184","mag":"2620725079"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2710184","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2710184","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5032951131","display_name":"Yuan\u2013Hsun Lo","orcid":"https://orcid.org/0000-0001-5510-8842"},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuan-Hsun Lo","raw_affiliation_strings":["School of Mathematical Sciences, Xiamen University, Xiamen, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Xiamen University, Xiamen, China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101907018","display_name":"Yijin Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yijin Zhang","raw_affiliation_strings":["National Mobile Communications Research Laboratory, Southeast University, Nanjing, China","School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"National Mobile Communications Research Laboratory, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100419212","display_name":"Yi Chen","orcid":"https://orcid.org/0000-0001-5616-2170"},"institutions":[{"id":"https://openalex.org/I4210099586","display_name":"Shenzhen Research Institute of Big Data","ror":"https://ror.org/00z1gwf89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210099586"]},{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Chen","raw_affiliation_strings":["School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China","Shenzhen Research Institute of Big Data, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"Shenzhen Research Institute of Big Data, Shenzhen, China","institution_ids":["https://openalex.org/I4210099586"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008893362","display_name":"Hung\u2010Lin Fu","orcid":"https://orcid.org/0000-0001-7218-3043"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Hung-Lin Fu","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039173605","display_name":"Wing Shing Wong","orcid":"https://orcid.org/0000-0001-6357-0981"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wing Shing Wong","raw_affiliation_strings":["Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Information Engineering, The Chinese University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032951131"],"corresponding_institution_ids":["https://openalex.org/I191208505"],"apc_list":null,"apc_paid":null,"fwci":1.7541,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.86733072,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"63","issue":"8","first_page":"5327","last_page":"5335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10847","display_name":"Advanced Optical Network Technologies","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10714","display_name":"Software-Defined Networks and 5G","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/clos-network","display_name":"Clos network","score":0.8833507895469666},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5356177091598511},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49772360920906067},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4693504273891449},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46464061737060547},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4622803032398224},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42798686027526855},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.42743194103240967},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.3871392011642456},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.37194764614105225},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35814064741134644},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0863831639289856}],"concepts":[{"id":"https://openalex.org/C119700423","wikidata":"https://www.wikidata.org/wiki/Q4418086","display_name":"Clos network","level":2,"score":0.8833507895469666},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5356177091598511},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49772360920906067},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4693504273891449},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46464061737060547},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4622803032398224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42798686027526855},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.42743194103240967},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3871392011642456},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.37194764614105225},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35814064741134644},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0863831639289856},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2017.2710184","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2710184","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5199999809265137,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[{"id":"https://openalex.org/G1883988674","display_name":null,"funder_award_id":"11601454","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3176976803","display_name":null,"funder_award_id":"2017D09","funder_id":"https://openalex.org/F4320324856","funder_display_name":"Southeast University"},{"id":"https://openalex.org/G5580882008","display_name":null,"funder_award_id":"61301107","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5804873015","display_name":null,"funder_award_id":"2016J05021","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G7084959127","display_name":null,"funder_award_id":"MOST 104-2115-M-009-009","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"},{"id":"https://openalex.org/G929272120","display_name":null,"funder_award_id":"YB2015100060","funder_id":"https://openalex.org/F4320322183","funder_display_name":"Huawei Technologies"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321878","display_name":"Natural Science Foundation of Fujian Province","ror":null},{"id":"https://openalex.org/F4320322183","display_name":"Huawei Technologies","ror":"https://ror.org/00cmhce21"},{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"},{"id":"https://openalex.org/F4320324856","display_name":"Southeast University","ror":"https://ror.org/04ct4d772"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W63654918","https://openalex.org/W1479863711","https://openalex.org/W1512052931","https://openalex.org/W1512138781","https://openalex.org/W1515357878","https://openalex.org/W1529323869","https://openalex.org/W1954214817","https://openalex.org/W1975751521","https://openalex.org/W1998471240","https://openalex.org/W2017402279","https://openalex.org/W2027090677","https://openalex.org/W2042876290","https://openalex.org/W2062207559","https://openalex.org/W2064810366","https://openalex.org/W2078691045","https://openalex.org/W2095183018","https://openalex.org/W2096313289","https://openalex.org/W2098124766","https://openalex.org/W2110317360","https://openalex.org/W2130531694","https://openalex.org/W2134316164","https://openalex.org/W2146117644","https://openalex.org/W2149804187","https://openalex.org/W2154984588","https://openalex.org/W2258813846","https://openalex.org/W2281738896","https://openalex.org/W2294352244","https://openalex.org/W3141776272","https://openalex.org/W4236424590","https://openalex.org/W4238465620","https://openalex.org/W6630823363"],"related_works":["https://openalex.org/W762363586","https://openalex.org/W1017987175","https://openalex.org/W4312744883","https://openalex.org/W1796112793","https://openalex.org/W1973224217","https://openalex.org/W3134800890","https://openalex.org/W4365808260","https://openalex.org/W2811511317","https://openalex.org/W2792302628","https://openalex.org/W1985727224"],"abstract_inverted_index":{"Data":[0],"centers":[1],"play":[2],"an":[3,78],"important":[4],"role":[5],"in":[6,86,134,182],"today's":[7],"Internet":[8],"development.":[9],"Research":[10],"to":[11,41,114,164,174,203,243,258,312],"find":[12],"scalable":[13],"architecture":[14],"and":[15,45,64,146,225,308,335],"efficient":[16],"routing":[17,53,75],"algorithms":[18,68],"for":[19,69,268],"data":[20],"center":[21],"networks":[22,269],"has":[23,39],"gained":[24],"popularity.":[25],"The":[26,100,184,230],"fat-tree":[27,56,306],"architecture,":[28],"which":[29,87],"is":[30,46,104,127,198,241,310],"essentially":[31],"a":[32,36,55,93,117,129,141,152,189,208],"folded":[33],"version":[34],"of":[35,72,108,154,160,167,177,188,207,234,288,303,316,323],"Clos":[37],"network,":[38,307],"proved":[40],"be":[42,151,244,313],"readily":[43],"implementable":[44],"scalable.":[47],"In":[48,137,256,275],"this":[49,263,276],"paper,":[50,277],"we":[51,278],"investigate":[52],"on":[54],"network":[57,80,113,342],"by":[58,65,111,194,238,280],"deriving":[59],"its":[60],"global":[61,101,185,231,285],"packing":[62,102,186,232,286],"number":[63,103,107,187,233,264,287],"presenting":[66],"explicit":[67,281],"the":[70,106,112,121,135,178,199,205,245,284,301,304,314,321,330],"construction":[71,283],"optimal,":[73],"load-balanced":[74,334],"solutions.":[76],"Consider":[77],"optical":[79,261],"that":[81,123,131,219,329],"employs":[82],"wavelength":[83,130,259],"division":[84,260,272],"multiplexing":[85],"every":[88,96],"user":[89,98],"node":[90,180],"sets":[91],"up":[92],"connection":[94,126],"with":[95,162],"other":[97],"node.":[99],"basically":[105],"wavelengths":[109],"required":[110],"support":[115],"such":[116,218],"traffic":[118],"load,":[119],"under":[120],"restriction":[122],"each":[124,176],"source-to-destination":[125],"assigned":[128],"remains":[132],"constant":[133],"network.":[136],"mathematical":[138],"terms,":[139],"consider":[140],"bidirectional,":[142],"simple":[143],"graph,":[144],"G":[145,161],"let":[147],"N":[148,165,309],"\u2286":[149],"V(G)":[150],"set":[153,315,322],"nodes.":[155],"A":[156],"path":[157,173,190,253],"system":[158,191],"P":[159,212,224],"respect":[163],"consists":[166],"|N|(|N|":[168],"-1)":[169],"directed":[170],"paths,":[171],"one":[172],"connect":[175],"source-destination":[179],"pairs":[181],"N.":[183],"P,":[192],"denoted":[193,237],"\u03a6(G,":[195,239,247],"N,":[196,248],"P),":[197],"minimum":[200,246],"integer":[201],"k":[202],"guarantee":[204],"existence":[206],"mapping":[209],"\u03c6":[210],":":[211],"\u2192":[213],"(1,":[214],"2,":[215],"...,":[216],"k),":[217],"\u03c6(P)":[220],"\u2260":[221],"\u03c6(P\u0305)":[222],"if":[223],"P\u0305":[226],"have":[227],"common":[228],"arc(s).":[229],"(G,":[235],"N),":[236,240,294],"defined":[242],"P)":[249],"among":[250],"all":[251,317,324,341],"possible":[252],"systems":[254],"?.":[255],"additional":[257],"networks,":[262],"also":[265],"carries":[266],"significance":[267],"employing":[270],"time":[271],"multiple":[273],"access.":[274],"compute":[279],"route":[282],"(T":[289],"<sub":[290,297],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[291,298],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[292,299],",":[293],"where":[295],"T":[296],"denotes":[300],"topology":[302],"n-ary":[305],"considered":[311],"edge":[318],"switches":[319],"or":[320],"supported":[325],"hosts.":[326],"We":[327],"show":[328],"constructed":[331],"routes":[332],"are":[333],"require":[336],"minimal":[337],"link":[338],"capacity":[339],"at":[340],"links.":[343]},"counts_by_year":[{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}