{"id":"https://openalex.org/W3150665916","doi":"https://doi.org/10.3934/amc.2021001","title":"An optimization approach to the Langberg-M\u00e9dard multiple unicast conjecture","display_name":"An optimization approach to the Langberg-M\u00e9dard multiple unicast conjecture","publication_year":2021,"publication_date":"2021-04-07","ids":{"openalex":"https://openalex.org/W3150665916","doi":"https://doi.org/10.3934/amc.2021001","mag":"3150665916"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2021001","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021001","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/amc.2021001","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":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kai Cai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5000081781","display_name":"Guangyue Han","orcid":"https://orcid.org/0000-0001-9895-5646"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guangyue Han","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102935428"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.464,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6493571,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"17","issue":"2","first_page":"431","last_page":"445"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9646999835968018,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9646999835968018,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9628999829292297,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9376000165939331,"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/mathematics","display_name":"Mathematics","score":0.822043240070343},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8132844567298889},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7196161150932312},{"id":"https://openalex.org/keywords/unicast","display_name":"Unicast","score":0.685558557510376},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4910461902618408},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18491151928901672},{"id":"https://openalex.org/keywords/multicast","display_name":"Multicast","score":0.061546534299850464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04626798629760742}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.822043240070343},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8132844567298889},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7196161150932312},{"id":"https://openalex.org/C11704745","wikidata":"https://www.wikidata.org/wiki/Q918337","display_name":"Unicast","level":3,"score":0.685558557510376},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4910461902618408},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18491151928901672},{"id":"https://openalex.org/C32295351","wikidata":"https://www.wikidata.org/wiki/Q899288","display_name":"Multicast","level":2,"score":0.061546534299850464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04626798629760742},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/amc.2021001","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021001","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/amc.2021001","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2021001","pdf_url":null,"source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1679422160","https://openalex.org/W1892667191","https://openalex.org/W1978601678","https://openalex.org/W1982221487","https://openalex.org/W1988191034","https://openalex.org/W2117341422","https://openalex.org/W2121205191","https://openalex.org/W2164808802","https://openalex.org/W2320258239","https://openalex.org/W2340149117","https://openalex.org/W2508558984","https://openalex.org/W2609828883","https://openalex.org/W2886134986","https://openalex.org/W3080345549","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1529715114","https://openalex.org/W1978042415","https://openalex.org/W3038654277","https://openalex.org/W3080345549","https://openalex.org/W2999121292","https://openalex.org/W3119737209","https://openalex.org/W3207412727","https://openalex.org/W4286901599","https://openalex.org/W3183820686","https://openalex.org/W1990400455"],"abstract_inverted_index":{"The":[0],"Langberg-M\u00e9dard":[1],"multiple":[2],"unicast":[3],"conjecture":[4],"claims":[5],"that":[6,38,78],"for":[7,56,93],"any":[8],"strongly":[9,58],"reachable":[10,59],"$":[11,21,32,36,42,46,60,67,74,81,84,94,98,105],"k":[12,61,106],"$-pair":[13,62],"network,":[14],"there":[15],"exists":[16],"a":[17,49],"multi-flow":[18,54,80],"with":[19],"rate":[20,55],"(1,1,\\dots,1)":[22],"$.":[23,112],"In":[24],"this":[25],"paper,":[26],"we":[27],"examine":[28],"an":[29],"optimization":[30],"problem":[31],"\\mathcal":[33,43,82,95],"P_{\\mathcal":[34,96],"S_k}":[35,45,71,97],"such":[37],"its":[39],"optimal":[40,92,100],"value":[41],"O_{\\mathcal":[44,70],"naturally":[47],"gives":[48],"lower":[50],"bound":[51],"on":[52],"the":[53,57,79],"network.":[63],"We":[64],"first":[65],"prove":[66],"\\lim_{k\\rightarrow":[68],"\\infty}\\mathcal":[69],"=":[72,107],"\\frac{9}{8}":[73],"and":[75,99,102],"then":[76],"show":[77],"C^*_k":[83],"constructed":[85],"in":[86],"our":[87],"previous":[88],"work":[89],"is":[90],"asymptotically":[91],"if":[101,104],"only":[103],"1,":[108],"2,":[109],"6,":[110],"10":[111]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
