{"id":"https://openalex.org/W1971506714","doi":"https://doi.org/10.1109/isit.2010.5513430","title":"A necessary and sufficient condition for solvability of a 3s/3t sum-network","display_name":"A necessary and sufficient condition for solvability of a 3s/3t sum-network","publication_year":2010,"publication_date":"2010-06-01","ids":{"openalex":"https://openalex.org/W1971506714","doi":"https://doi.org/10.1109/isit.2010.5513430","mag":"1971506714"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2010.5513430","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513430","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","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/A5064788219","display_name":"Sagar Shenvi","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Sagar Shenvi","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India, 400 076"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India, 400 076","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064926409","display_name":"Bikash Kumar Dey","orcid":"https://orcid.org/0000-0003-0333-2257"},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bikash Kumar Dey","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India, 400 076"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]},{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Technology Bombay, Mumbai, India, 400 076","institution_ids":["https://openalex.org/I162827531"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064788219"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":null,"apc_paid":null,"fwci":2.1368,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.87171497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"1858","last_page":"1862"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":1.0,"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":1.0,"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/T10148","display_name":"Advanced MIMO Systems Optimization","score":0.9962000250816345,"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/T11458","display_name":"Advanced Wireless Communication Technologies","score":0.9962000250816345,"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/terminal","display_name":"Terminal (telecommunication)","score":0.660062849521637},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.6561078429222107},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6013340950012207},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5460240840911865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5242717266082764},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5165113806724548},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47020822763442993},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.43126463890075684},{"id":"https://openalex.org/keywords/linear-network-coding","display_name":"Linear network coding","score":0.4125676155090332},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3904322683811188},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.1645171344280243},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.14866870641708374},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.062323182821273804},{"id":"https://openalex.org/keywords/network-packet","display_name":"Network packet","score":0.055916935205459595}],"concepts":[{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.660062849521637},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.6561078429222107},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6013340950012207},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5460240840911865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5242717266082764},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5165113806724548},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47020822763442993},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.43126463890075684},{"id":"https://openalex.org/C138293262","wikidata":"https://www.wikidata.org/wiki/Q1089578","display_name":"Linear network coding","level":3,"score":0.4125676155090332},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3904322683811188},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.1645171344280243},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.14866870641708374},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.062323182821273804},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.055916935205459595},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2010.5513430","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2010.5513430","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"},{"id":"pmh:oai:dsapce.library.iitb.ac.in:100/2321","is_oa":false,"landing_page_url":"http://doi.org/10.1109/ISIT.2010.5513430","pdf_url":null,"source":{"id":"https://openalex.org/S4306400899","display_name":"DSpace (IIT Bombay)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I162827531","host_organization_name":"Indian Institute of Technology Bombay","host_organization_lineage":["https://openalex.org/I162827531"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2010 IEEE International Symposium on Information Theory,Austin, TX,JUL 13-13, 2010","raw_type":"Proceedings Paper"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W51132397","https://openalex.org/W177399933","https://openalex.org/W1626312869","https://openalex.org/W1768290500","https://openalex.org/W2019307453","https://openalex.org/W2048235391","https://openalex.org/W2053269541","https://openalex.org/W2096342910","https://openalex.org/W2104973644","https://openalex.org/W2105831729","https://openalex.org/W2106403318","https://openalex.org/W2110540512","https://openalex.org/W2123562143","https://openalex.org/W2138928022","https://openalex.org/W2148800638","https://openalex.org/W2159572035","https://openalex.org/W2209179758","https://openalex.org/W2266819685","https://openalex.org/W2539443493","https://openalex.org/W2963305818","https://openalex.org/W4212896000","https://openalex.org/W4295307008"],"related_works":["https://openalex.org/W3211557223","https://openalex.org/W1528816634","https://openalex.org/W2007036916","https://openalex.org/W4206528302","https://openalex.org/W872563264","https://openalex.org/W2164087676","https://openalex.org/W2389793738","https://openalex.org/W2962934782","https://openalex.org/W2964326893","https://openalex.org/W1978343121"],"abstract_inverted_index":{"We":[0,55,65,92,124],"consider":[1],"a":[2,21,58,60,67,73,127,134],"directed":[3],"acyclic":[4],"network":[5,59],"with":[6],"three":[7,10],"sources":[8,121],"and":[9,25,44,69,97,122],"terminals":[11],"such":[12,57],"that":[13,94,130],"each":[14,26,53],"source":[15,37],"independently":[16],"generates":[17],"one":[18,47],"symbol":[19,48],"from":[20,49],"given":[22],"field":[23,51],"F":[24],"terminal":[27],"wants":[28],"to":[29,76,114],"receive":[30],"the":[31,36,50,90,131],"sum":[32],"(over":[33],"F)":[34],"of":[35,120,133],"symbols.":[38],"Each":[39],"link":[40],"is":[41,137],"error-free,":[42],"delay-free":[43],"can":[45],"carry":[46],"in":[52,98],"use.":[54],"call":[56],"3-source":[61],"3-terminal":[62],"(3s/3t)":[63],"sum-network.":[64],"give":[66],"necessary":[68],"sufficient":[70,87,104],"condition":[71],"for":[72,89,105,108,117],"3s/3t":[74,109,135],"sum-network":[75,136],"be":[77,115],"solvable":[78],"over":[79],"any":[80],"field.":[81],"Some":[82],"lemmas":[83],"provide":[84],"interesting":[85],"simpler":[86],"conditions":[88],"same.":[91],"show":[93],"linear":[95],"codes,":[96,102],"most":[99],"cases":[100],"XOR":[101],"are":[103,112],"this":[106],"problem":[107],"though":[110],"they":[111],"known":[113],"insufficient":[116],"arbitrary":[118],"number":[119],"terminals.":[123],"also":[125],"prove":[126],"recent":[128],"conjecture":[129],"capacity":[132],"either":[138],"0,":[139],"2/3":[140],"or":[141],"\u2265":[142],"1.":[143]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}