{"id":"https://openalex.org/W1551197376","doi":"https://doi.org/10.1109/icc.2015.7249021","title":"A necessary and sufficient closure property for two-stage constructions of switching networks","display_name":"A necessary and sufficient closure property for two-stage constructions of switching networks","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W1551197376","doi":"https://doi.org/10.1109/icc.2015.7249021","mag":"1551197376"},"language":"en","primary_location":{"id":"doi:10.1109/icc.2015.7249021","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icc.2015.7249021","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Communications (ICC)","raw_type":"proceedings-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/A5111448700","display_name":"Ching-Min Lien","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Ching-Min Lien","raw_affiliation_strings":["Institute of Communications Engineering National Tsing Hua University, Hsinchu, Taiwan R.O.C","Institute of Communications Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan, R.O.C"],"affiliations":[{"raw_affiliation_string":"Institute of Communications Engineering National Tsing Hua University, Hsinchu, Taiwan R.O.C","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"Institute of Communications Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan, R.O.C","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016945609","display_name":"Cheng\u2010Shang Chang","orcid":"https://orcid.org/0000-0002-5386-4756"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Cheng-Shang Chang","raw_affiliation_strings":["Institute of Communications Engineering National Tsing Hua University, Hsinchu, Taiwan R.O.C","Institute of Communications Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan, R.O.C"],"affiliations":[{"raw_affiliation_string":"Institute of Communications Engineering National Tsing Hua University, Hsinchu, Taiwan R.O.C","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"Institute of Communications Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan, R.O.C","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043136272","display_name":"Duan\u2010Shin Lee","orcid":"https://orcid.org/0000-0003-4578-2002"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Duan-Shin Lee","raw_affiliation_strings":["Institute of Communications Engineering National Tsing Hua University, Hsinchu, Taiwan R.O.C","Institute of Communications Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan, R.O.C"],"affiliations":[{"raw_affiliation_string":"Institute of Communications Engineering National Tsing Hua University, Hsinchu, Taiwan R.O.C","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"Institute of Communications Engineering, National Tsing Hua University, Hsinchu, 30013, Taiwan, R.O.C","institution_ids":["https://openalex.org/I25846049"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111448700"],"corresponding_institution_ids":["https://openalex.org/I25846049"],"apc_list":null,"apc_paid":null,"fwci":0.7007,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73828619,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"4437","last_page":"4442"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"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":0.9997000098228455,"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9929999709129333,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.9890000224113464,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/banyan","display_name":"Banyan","score":0.925533652305603},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.803722620010376},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.7439210414886475},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5716351270675659},{"id":"https://openalex.org/keywords/multistage-interconnection-networks","display_name":"Multistage interconnection networks","score":0.5460138916969299},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.528460681438446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5094624161720276},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.47133684158325195},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.4427647292613983},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41675305366516113},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.365352988243103},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33520442247390747},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.21163681149482727},{"id":"https://openalex.org/keywords/interconnection","display_name":"Interconnection","score":0.14125490188598633},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0805700421333313}],"concepts":[{"id":"https://openalex.org/C2780435913","wikidata":"https://www.wikidata.org/wiki/Q465570","display_name":"Banyan","level":2,"score":0.925533652305603},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.803722620010376},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.7439210414886475},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5716351270675659},{"id":"https://openalex.org/C2776832011","wikidata":"https://www.wikidata.org/wiki/Q6935099","display_name":"Multistage interconnection networks","level":3,"score":0.5460138916969299},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.528460681438446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5094624161720276},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.47133684158325195},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.4427647292613983},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41675305366516113},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.365352988243103},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33520442247390747},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.21163681149482727},{"id":"https://openalex.org/C123745756","wikidata":"https://www.wikidata.org/wiki/Q1665949","display_name":"Interconnection","level":2,"score":0.14125490188598633},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0805700421333313},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/icc.2015.7249021","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icc.2015.7249021","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Communications (ICC)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.714.707","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.714.707","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ee.nthu.edu.tw/cschang/twostageICC2015final.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.7599999904632568,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W74326264","https://openalex.org/W1482318866","https://openalex.org/W1551197376","https://openalex.org/W1598492279","https://openalex.org/W1995021131","https://openalex.org/W2028613093","https://openalex.org/W2042876290","https://openalex.org/W2067692201","https://openalex.org/W2071274877","https://openalex.org/W2096313289","https://openalex.org/W2105413189","https://openalex.org/W2113267039","https://openalex.org/W2117358494","https://openalex.org/W2121621147","https://openalex.org/W2134316164","https://openalex.org/W2155809496","https://openalex.org/W2163763959","https://openalex.org/W2486673534","https://openalex.org/W3017089570","https://openalex.org/W4298269868","https://openalex.org/W6633084408","https://openalex.org/W6674690999"],"related_works":["https://openalex.org/W11362006","https://openalex.org/W2128853291","https://openalex.org/W2215461297","https://openalex.org/W1987749257","https://openalex.org/W1569023040","https://openalex.org/W4238197572","https://openalex.org/W2153800715","https://openalex.org/W2073811724","https://openalex.org/W1983047968","https://openalex.org/W1587112450"],"abstract_inverted_index":{"Two-stage":[0],"constructions":[1,19,131,246],"and":[2,20,28,103,122,152,166,199,209,220,275],"banyan-type":[3,21,238,263],"networks":[4,22,239],"play":[5],"important":[6],"roles":[7],"in":[8,51,100,111],"designing":[9],"high":[10],"speed":[11],"switch":[12,69,187,197],"fabrics.":[13],"Switch":[14],"fabrics":[15],"designed":[16],"from":[17,71],"two-stage":[18,53,73,130,143,157,191,235,245],"cannot":[23],"realize":[24,56,77,176],"all":[25,48,202],"the":[26,43,49,68,72,84,97,101,104,108,137,177,203,206,210,228],"permutations":[27,60,81,138,165,229],"are":[29,140,213,240],"known":[30],"as":[31,132,171,265],"conditionally":[32,39],"nonblocking":[33,40],"switches.":[34,216],"A":[35],"renowned":[36],"property":[37,65,86,92,155],"for":[38,96,156,257],"switches":[41,50,170,172,204],"is":[42,93,110,125,193],"closure":[44,91,154],"property,":[45],"i.e.,":[46],"if":[47,198,201],"a":[52,57,63,78,90,120,150,186,190,194,218,224,254,266,271],"construction":[54,74,192],"can":[55,75,134,174,231],"subset":[58,79],"of":[59,80,107,126,179,227,261,268],"that":[61,82,139,173,185,230],"satisfy":[62,83],"certain":[64],"P,":[66],"then":[67],"resulted":[70],"also":[76],"same":[85],"P.":[87],"However,":[88],"such":[89,119],"mostly":[94],"stated":[95],"sufficient":[98,123,153,221],"part":[99,106],"literature":[102],"necessary":[105,121,151,219],"statement":[109],"general":[112],"either":[113],"not":[114],"true":[115],"or":[116],"unknown.":[117],"Finding":[118],"result":[124,222],"fundamental":[127],"importance":[128],"to":[129],"it":[133],"completely":[135],"characterize":[136],"realizable":[141,259],"by":[142,189,234,243],"constructions.":[144,158,236],"In":[145],"this":[146],"paper,":[147],"we":[148,161,252],"prove":[149],"For":[159],"this,":[160],"consider":[162],"uniform":[163,168,180,195,214,272],"mapping":[164,169,181,196,215,273],"define":[167],"only":[175,200],"set":[178],"permutations.":[182],"We":[183],"show":[184],"constructed":[188,241],"at":[205],"first":[207],"stage":[208,212],"second":[211],"Such":[217],"provides":[223],"complete":[225,255],"characterization":[226,256],"be":[232],"realized":[233],"Since":[237],"recursively":[242],"using":[244],"with":[247],"2":[248,250],"\u00d7":[249],"switches,":[251],"obtain":[253],"any":[258,262],"permutation":[260,274],"network":[264],"composition":[267],"its":[269,276],"trace,":[270],"guide.":[277]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
