{"id":"https://openalex.org/W4214681728","doi":"https://doi.org/10.1109/tit.2022.3154230","title":"The Langberg-M\u00e9dard Multiple Unicast Conjecture for 3-Pair Networks","display_name":"The Langberg-M\u00e9dard Multiple Unicast Conjecture for 3-Pair Networks","publication_year":2022,"publication_date":"2022-02-24","ids":{"openalex":"https://openalex.org/W4214681728","doi":"https://doi.org/10.1109/tit.2022.3154230"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3154230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3154230","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/A5102935428","display_name":"Kai Cai","orcid":"https://orcid.org/0000-0002-8798-8650"},"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":"Kai Cai","raw_affiliation_strings":["Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000081781","display_name":"Guangyue Han","orcid":"https://orcid.org/0000-0001-9895-5646"},"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":false,"raw_author_name":"Guangyue Han","raw_affiliation_strings":["Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102935428"],"corresponding_institution_ids":["https://openalex.org/I889458895"],"apc_list":null,"apc_paid":null,"fwci":0.2761,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.53482234,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"68","issue":"6","first_page":"3879","last_page":"3895"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9995999932289124,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9995999932289124,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9805999994277954,"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/T11716","display_name":"Random Matrices and Applications","score":0.9496999979019165,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.819652259349823},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.7799285650253296},{"id":"https://openalex.org/keywords/unicast","display_name":"Unicast","score":0.5393223166465759},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5057189464569092},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45950835943222046},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37646016478538513},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32772567868232727},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12841761112213135}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.819652259349823},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7799285650253296},{"id":"https://openalex.org/C11704745","wikidata":"https://www.wikidata.org/wiki/Q918337","display_name":"Unicast","level":3,"score":0.5393223166465759},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5057189464569092},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45950835943222046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37646016478538513},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32772567868232727},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12841761112213135},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3154230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3154230","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":[],"awards":[{"id":"https://openalex.org/G2690108622","display_name":null,"funder_award_id":"61871343","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G708152933","display_name":null,"funder_award_id":"17304121","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G7083589740","display_name":null,"funder_award_id":"17301017","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W69045515","https://openalex.org/W1679422160","https://openalex.org/W1978601678","https://openalex.org/W1982221487","https://openalex.org/W1988191034","https://openalex.org/W2029686768","https://openalex.org/W2117341422","https://openalex.org/W2121205191","https://openalex.org/W2133500866","https://openalex.org/W2164808802","https://openalex.org/W2325997012","https://openalex.org/W2508558984","https://openalex.org/W2609828883","https://openalex.org/W2767454305","https://openalex.org/W2886134986","https://openalex.org/W3080345549","https://openalex.org/W3150665916","https://openalex.org/W4297399141"],"related_works":["https://openalex.org/W2508558984","https://openalex.org/W4288633135","https://openalex.org/W2952300997","https://openalex.org/W2910872135","https://openalex.org/W2794998165","https://openalex.org/W2378130666","https://openalex.org/W2615656263","https://openalex.org/W3008817519","https://openalex.org/W2052662459","https://openalex.org/W2363154745"],"abstract_inverted_index":{"The":[0],"Langberg-M\u00e9dard":[1],"multiple":[2],"unicast":[3],"conjecture":[4,41],"claims":[5],"that":[6],"for":[7,42],"a":[8,21],"strongly":[9],"reachable":[10],"<inline-formula":[11,26,43],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[12,27,44],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[13,28,45],"<tex-math":[14,29,46],"notation=\"LaTeX\">$k$":[15],"</tex-math></inline-formula>":[16,33,48],"-pair":[17],"network,":[18],"there":[19],"exists":[20],"feasible":[22],"multi-flow":[23],"with":[24],"rate":[25],"notation=\"LaTeX\">$(1,1,":[30],"{\\dots":[31],"},1)$":[32],".":[34,49],"In":[35],"this":[36],"paper,":[37],"we":[38],"confirm":[39],"the":[40],"notation=\"LaTeX\">$k=3$":[47]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
