{"id":"https://openalex.org/W2140448484","doi":"https://doi.org/10.1137/0221048","title":"Increasing the Size of a Network by a Constant Factor can Increase Performance by More Than a Constant Factor","display_name":"Increasing the Size of a Network by a Constant Factor can Increase Performance by More Than a Constant Factor","publication_year":1992,"publication_date":"1992-10-01","ids":{"openalex":"https://openalex.org/W2140448484","doi":"https://doi.org/10.1137/0221048","mag":"2140448484"},"language":"en","primary_location":{"id":"doi:10.1137/0221048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0221048","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/A5080729700","display_name":"Richard Koch","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Richard Koch","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080729700"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9423,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.79510978,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"5","first_page":"801","last_page":"823"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":1.0,"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":1.0,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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":0.9871000051498413,"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/combinatorics","display_name":"Combinatorics","score":0.5765445232391357},{"id":"https://openalex.org/keywords/queue","display_name":"Queue","score":0.5420042872428894},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5353795289993286},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5230342149734497},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.4958229959011078},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4836936593055725},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.45590633153915405},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4554341733455658},{"id":"https://openalex.org/keywords/traverse","display_name":"Traverse","score":0.44957032799720764},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43792372941970825},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.4253152310848236},{"id":"https://openalex.org/keywords/interconnection","display_name":"Interconnection","score":0.41311872005462646},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.2543970048427582}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5765445232391357},{"id":"https://openalex.org/C160403385","wikidata":"https://www.wikidata.org/wiki/Q220543","display_name":"Queue","level":2,"score":0.5420042872428894},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5353795289993286},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5230342149734497},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.4958229959011078},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4836936593055725},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.45590633153915405},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4554341733455658},{"id":"https://openalex.org/C176809094","wikidata":"https://www.wikidata.org/wiki/Q15401496","display_name":"Traverse","level":2,"score":0.44957032799720764},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43792372941970825},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.4253152310848236},{"id":"https://openalex.org/C123745756","wikidata":"https://www.wikidata.org/wiki/Q1665949","display_name":"Interconnection","level":2,"score":0.41311872005462646},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.2543970048427582},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0221048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0221048","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1987749257","https://openalex.org/W2006544720","https://openalex.org/W2006551925","https://openalex.org/W2015913288","https://openalex.org/W2044548351","https://openalex.org/W2097415784","https://openalex.org/W2113356772","https://openalex.org/W2132733020","https://openalex.org/W2164309468","https://openalex.org/W2167266655"],"related_works":["https://openalex.org/W2377402383","https://openalex.org/W2380835401","https://openalex.org/W2381912691","https://openalex.org/W2350381577","https://openalex.org/W2353618196","https://openalex.org/W2348074676","https://openalex.org/W2385033175","https://openalex.org/W2374043190","https://openalex.org/W2363298784","https://openalex.org/W2367402697"],"abstract_inverted_index":{"The":[0,52,145,260],"performance":[1],"of":[2,20,25,71,84,88,117,142,150,214,255,258,278,283,293],"unbuffered":[3],"routing":[4,59],"algorithms":[5,13],"for":[6,58,198,207,230,252,266,270],"parallel":[7],"computer":[8],"architectures":[9],"is":[10,31,56,104,138,147,157,172,190,227,236,242],"analyzed.":[11],"Unbuffered":[12],"are":[14,36,135,250],"an":[15,114,128],"alternative":[16],"to":[17,41,93,106,126],"the":[18,23,33,43,61,78,85,89,102,130,140,143,148,169,187,203,231,239,281,291],"use":[19],"queues.":[21],"When":[22],"capacity":[24],"a":[26,49,95,107,275],"switch":[27],"or":[28,295],"communications":[29],"link":[30],"exceeded,":[32],"extra":[34,131],"messages":[35,124,132,151],"discarded,":[37],"and":[38,64,66,100,178,206,216,220,234],"another":[39],"attempt":[40,125],"transmit":[42],"message":[44,96,103],"will":[45,285],"be":[46],"made":[47],"at":[48],"later":[50],"time.":[51],"analysis":[53],"presented":[54],"here":[55],"relevant":[57],"on":[60,77,202],"BBN":[62],"Butterfly":[63],"Agarwal":[65],"Knight\u2019s":[67],"Alewife":[68],"architecture,":[69],"both":[70],"which":[72],"have":[73,264],"interconnection":[74],"networks":[75,200],"based":[76,201],"butterfly":[79,90,205],"graph.":[80],"Suppose":[81],"that":[82,101,152,159,238],"each":[83,111],"N":[86],"inputs":[87,219],"independently":[91],"decides":[92],"send":[94],"with":[97,110],"probability":[98,116,240],"p,":[99],"sent":[105],"random":[108],"output,":[109],"output":[112],"having":[113,274],"equal":[115],"being":[118],"chosen.":[119],"If":[120],"more":[121,288],"than":[122,289],"q":[123,134,137,284],"traverse":[127],"edge,":[129],"over":[133],"discarded.":[136],"called":[139],"dilation":[141],"network.":[144],"bandwidth":[146,171,189,287],"number":[149],"reach":[153],"their":[154],"destinations.":[155],"It":[156],"shown":[158,237],"if":[160,179],"$p":[161,180],"=":[162,181],"\\Omega":[163],"((\\log":[164],"N)^{":[165,175,183],"-":[166,176,184],"1/q}":[167,185],")$,":[168,186],"expected":[170,188],"$\\Theta":[173],"(N(\\log":[174],"1/q})$,":[177],"o((\\log":[182],"$N(p":[191],"+":[192],"o(p))$.":[193],"This":[194],"result":[195,261],"also":[196,221,228,263],"holds":[197],"dilated":[199],"d-ary":[204],"graphs":[208],"constructed":[209],"by":[210],"taking":[211],"r":[212],"copies":[213],"butterflies":[215],"identifying":[217,222],"corresponding":[218,223],"outputs.":[224],"An":[225],"expression":[226],"derived":[229],"asymptotic":[232],"constants":[233],"it":[235],"distribution":[241],"tightly":[243],"concentrated":[244],"about":[245],"its":[246],"mean.":[247],"Interesting":[248],"techniques":[249],"developed":[251],"finding":[253],"asymptotics":[254],"nonlinear":[256],"systems":[257],"recurrences.":[259],"may":[262],"implications":[265],"design":[267],"trade-offs":[268],"since,":[269],"sufficiently":[271],"large":[272],"networks,":[273],"fixed":[276],"amount":[277],"hardware":[279],"increasing":[280,290],"value":[282],"increase":[286],"values":[292],"d":[294],"r.":[296]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}