{"id":"https://openalex.org/W2976539725","doi":"https://doi.org/10.1109/isit.2019.8849369","title":"On the Complexity of Computing the Shannon Outer Bound to a Network Coding Capacity Region","display_name":"On the Complexity of Computing the Shannon Outer Bound to a Network Coding Capacity Region","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2976539725","doi":"https://doi.org/10.1109/isit.2019.8849369","mag":"2976539725"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2019.8849369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849369","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","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/A5040872851","display_name":"Yirui Liu","orcid":"https://orcid.org/0009-0002-5794-9682"},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yirui Liu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, 19104, USA","Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, 19104, USA","institution_ids":["https://openalex.org/I72816309"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I72816309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060945955","display_name":"John MacLaren Walsh","orcid":null},"institutions":[{"id":"https://openalex.org/I72816309","display_name":"Drexel University","ror":"https://ror.org/04bdffz58","country_code":"US","type":"education","lineage":["https://openalex.org/I72816309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John MacLaren Walsh","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, 19104, USA","Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, 19104, USA","institution_ids":["https://openalex.org/I72816309"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Drexel University, Philadelphia, PA, USA","institution_ids":["https://openalex.org/I72816309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040872851"],"corresponding_institution_ids":["https://openalex.org/I72816309"],"apc_list":null,"apc_paid":null,"fwci":0.1853,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56331412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":"206","last_page":"210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9998999834060669,"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":0.9998999834060669,"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/T11321","display_name":"Error Correcting Code Techniques","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/T12162","display_name":"Cellular Automata and Applications","score":0.9986000061035156,"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/computer-science","display_name":"Computer science","score":0.6598971486091614},{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.5471129417419434},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5204418301582336},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4241583049297333},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.39751991629600525},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.2790387272834778},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2179308831691742},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08660203218460083}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6598971486091614},{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.5471129417419434},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5204418301582336},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4241583049297333},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39751991629600525},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.2790387272834778},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2179308831691742},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08660203218460083},{"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/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/isit.2019.8849369","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2019.8849369","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1495145358","https://openalex.org/W1526262508","https://openalex.org/W1976579642","https://openalex.org/W2034443872","https://openalex.org/W2037067936","https://openalex.org/W2037413426","https://openalex.org/W2052977643","https://openalex.org/W2059865055","https://openalex.org/W2060472508","https://openalex.org/W2086387649","https://openalex.org/W2095127695","https://openalex.org/W2105185344","https://openalex.org/W2128465722","https://openalex.org/W2138744797","https://openalex.org/W2216809397","https://openalex.org/W2262362834","https://openalex.org/W2405694149","https://openalex.org/W2502673344","https://openalex.org/W2547052808","https://openalex.org/W2555631965","https://openalex.org/W2627099791","https://openalex.org/W2949982710","https://openalex.org/W2962901739","https://openalex.org/W2964195131","https://openalex.org/W3106164725","https://openalex.org/W6665615197","https://openalex.org/W6679111848","https://openalex.org/W6713708239","https://openalex.org/W6724810792","https://openalex.org/W6740101039"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2212571888","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052","https://openalex.org/W2134859306"],"abstract_inverted_index":{"A":[0],"new":[1,37],"method":[2],"is":[3],"presented,":[4],"consisting":[5],"of":[6,26,45],"exclusively":[7],"simple":[8],"linear":[9,15,32],"algebra":[10],"computations,":[11],"for":[12],"computing":[13,46],"the":[14,21,41,47],"programming":[16],"Shannon":[17,48],"outer":[18,49],"bound":[19,39,50],"to":[20,51,57],"network":[22,53],"coding":[23,54],"capacity":[24,55],"region":[25,56],"a":[27,36,52],"directed":[28],"hypergraph":[29],"network.":[30],"This":[31],"algebraic":[33],"formulation":[34],"enables":[35],"upper":[38],"on":[40],"worst":[42],"case":[43],"complexity":[44],"be":[58],"determined.":[59]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}