{"id":"https://openalex.org/W2077906216","doi":"https://doi.org/10.1002/(sici)1097-0037(199907)33:4<261::aid-net3>3.0.co;2-q","title":"Characterizing bit permutation networks","display_name":"Characterizing bit permutation networks","publication_year":1999,"publication_date":"1999-07-01","ids":{"openalex":"https://openalex.org/W2077906216","doi":"https://doi.org/10.1002/(sici)1097-0037(199907)33:4<261::aid-net3>3.0.co;2-q","mag":"2077906216"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0037(199907)33:4<261::aid-net3>3.0.co;2-q","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0037(199907)33:4<261::aid-net3>3.0.co;2-q","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5002508116","display_name":"Gerard J. Chang","orcid":null},"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":true,"raw_author_name":"Gerard J. Chang","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103573008","display_name":"Frank K. Hwang","orcid":null},"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":"Frank K. Hwang","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110130086","display_name":"Li-Da Tong","orcid":null},"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":"Li-Da Tong","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002508116"],"corresponding_institution_ids":["https://openalex.org/I148366613"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":1.546,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.86365644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"33","issue":"4","first_page":"261","last_page":"267"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9994000196456909,"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":0.9994000196456909,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9588000178337097,"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/T11009","display_name":"Catalysis for Biomass Conversion","score":0.940500020980835,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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":0.8925038576126099},{"id":"https://openalex.org/keywords/multistage-interconnection-networks","display_name":"Multistage interconnection networks","score":0.7567920684814453},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6733834147453308},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6627766489982605},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5797315239906311},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5186883211135864},{"id":"https://openalex.org/keywords/interconnection","display_name":"Interconnection","score":0.5112514495849609},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.44518065452575684},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4391497075557709},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.42858368158340454},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3805869519710541},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.3505275547504425},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34213826060295105},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3375118374824524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32553020119667053},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07799434661865234}],"concepts":[{"id":"https://openalex.org/C2780435913","wikidata":"https://www.wikidata.org/wiki/Q465570","display_name":"Banyan","level":2,"score":0.8925038576126099},{"id":"https://openalex.org/C2776832011","wikidata":"https://www.wikidata.org/wiki/Q6935099","display_name":"Multistage interconnection networks","level":3,"score":0.7567920684814453},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6733834147453308},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6627766489982605},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5797315239906311},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5186883211135864},{"id":"https://openalex.org/C123745756","wikidata":"https://www.wikidata.org/wiki/Q1665949","display_name":"Interconnection","level":2,"score":0.5112514495849609},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44518065452575684},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4391497075557709},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.42858368158340454},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3805869519710541},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3505275547504425},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34213826060295105},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3375118374824524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32553020119667053},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07799434661865234},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0037(199907)33:4<261::aid-net3>3.0.co;2-q","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0037(199907)33:4<261::aid-net3>3.0.co;2-q","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.4399999976158142,"id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1973383391","https://openalex.org/W1984110971","https://openalex.org/W1996349829","https://openalex.org/W2044548351","https://openalex.org/W2116454746","https://openalex.org/W2134484974","https://openalex.org/W2154307687","https://openalex.org/W2168961449"],"related_works":["https://openalex.org/W2128853291","https://openalex.org/W11362006","https://openalex.org/W2215461297","https://openalex.org/W1987749257","https://openalex.org/W2189226368","https://openalex.org/W2153800715","https://openalex.org/W4321520003","https://openalex.org/W4238197572","https://openalex.org/W1569023040","https://openalex.org/W1897112082"],"abstract_inverted_index":{"In":[0,81],"recent":[1],"years,":[2],"many":[3],"multistage":[4],"interconnection":[5],"networks":[6,33,37,49,108],"using":[7],"2":[8,10],"\u00d7":[9],"switching":[11],"elements":[12],"have":[13,41],"been":[14,43],"proposed":[15],"for":[16],"parallel":[17],"architectures.":[18],"Typical":[19],"examples":[20],"are":[21,34,63],"baseline":[22],"networks,":[23,25,27,61,91],"banyan":[24],"shuffle-exchange":[26],"and":[28,50],"their":[29],"inverses.":[30],"As":[31],"these":[32,79],"blocking,":[35],"such":[36,107],"with":[38],"extra":[39],"stages":[40],"also":[42,71],"studied":[44,59,85],"extensively.":[45],"These":[46],"include":[47],"Benes":[48],"\u0394":[51],"\u2295":[52],"\u0394\u2032":[53],"networks.":[54,69,80,101],"Recently,":[55],"Hwang":[56],"et":[57],"al.":[58],"k-extra-stage":[60],"which":[62,92],"a":[64,86],"generalization":[65],"of":[66,78,90,106,111],"the":[67,73,104],"above":[68],"They":[70],"investigated":[72],"equivalence":[74,105],"issue":[75],"among":[76],"some":[77],"this":[82],"paper,":[83],"we":[84,93],"more":[87],"general":[88],"class":[89],"call":[94],"(m":[95],"+":[96],"1)-stage":[97],"d-nary":[98],"bit":[99],"permutation":[100],"We":[102],"characterize":[103],"by":[109],"sequence":[110],"positive":[112],"integers.":[113],"\u00a9":[114],"1999":[115,124],"John":[116],"Wiley":[117],"&":[118],"Sons,":[119],"Inc.":[120],"Networks":[121],"33:":[122],"261\u2013267,":[123]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
