{"id":"https://openalex.org/W2091480483","doi":"https://doi.org/10.5539/cis.v8n2p1","title":"Comparing Algorithms for Minimizing Congestion and Cost in the Multi-Commodity k-Splittable Flow","display_name":"Comparing Algorithms for Minimizing Congestion and Cost in the Multi-Commodity k-Splittable Flow","publication_year":2015,"publication_date":"2015-04-05","ids":{"openalex":"https://openalex.org/W2091480483","doi":"https://doi.org/10.5539/cis.v8n2p1","mag":"2091480483"},"language":"en","primary_location":{"id":"doi:10.5539/cis.v8n2p1","is_oa":true,"landing_page_url":"https://doi.org/10.5539/cis.v8n2p1","pdf_url":"http://www.ccsenet.org/journal/index.php/cis/article/download/47278/25533","source":{"id":"https://openalex.org/S2764452479","display_name":"Computer and Information Science","issn_l":"1913-8989","issn":["1913-8989","1913-8997"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322531","host_organization_name":"Canadian Center of Science and Education","host_organization_lineage":["https://openalex.org/P4310322531"],"host_organization_lineage_names":["Canadian Center of Science and Education"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer and Information Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"http://www.ccsenet.org/journal/index.php/cis/article/download/47278/25533","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040643167","display_name":"Chengwen Jiao","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chengwen Jiao","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008469096","display_name":"Suixiang Gao","orcid":"https://orcid.org/0000-0002-2934-5091"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Suixiang Gao","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","[University of the Chinese Academy of Sciences]"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"[University of the Chinese Academy of Sciences]","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084332010","display_name":"Wenguo Yang","orcid":"https://orcid.org/0000-0002-8441-7334"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenguo Yang","raw_affiliation_strings":["School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5084332010"],"corresponding_institution_ids":["https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":1.1515,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.81898479,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"8","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T11502","display_name":"Facility Location and Emergency Management","score":0.97079998254776,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.964900016784668,"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":0.8306492567062378},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.6690646409988403},{"id":"https://openalex.org/keywords/minimum-cost-flow-problem","display_name":"Minimum-cost flow problem","score":0.6253415942192078},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5894826054573059},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.5702418088912964},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5202047228813171},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.512409508228302},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49589356780052185},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.49270036816596985},{"id":"https://openalex.org/keywords/network-congestion","display_name":"Network congestion","score":0.4403077960014343},{"id":"https://openalex.org/keywords/commodity","display_name":"Commodity","score":0.4348943829536438},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14207535982131958},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.09480223059654236},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.08258771896362305},{"id":"https://openalex.org/keywords/network-packet","display_name":"Network packet","score":0.06593924760818481},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06584993004798889},{"id":"https://openalex.org/keywords/computer-security","display_name":"Computer security","score":0.05811351537704468}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8306492567062378},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.6690646409988403},{"id":"https://openalex.org/C99545648","wikidata":"https://www.wikidata.org/wiki/Q2897180","display_name":"Minimum-cost flow problem","level":3,"score":0.6253415942192078},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5894826054573059},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.5702418088912964},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5202047228813171},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.512409508228302},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49589356780052185},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.49270036816596985},{"id":"https://openalex.org/C195563490","wikidata":"https://www.wikidata.org/wiki/Q180368","display_name":"Network congestion","level":3,"score":0.4403077960014343},{"id":"https://openalex.org/C2779439359","wikidata":"https://www.wikidata.org/wiki/Q317088","display_name":"Commodity","level":2,"score":0.4348943829536438},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14207535982131958},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.09480223059654236},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08258771896362305},{"id":"https://openalex.org/C158379750","wikidata":"https://www.wikidata.org/wiki/Q214111","display_name":"Network packet","level":2,"score":0.06593924760818481},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06584993004798889},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.05811351537704468},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5539/cis.v8n2p1","is_oa":true,"landing_page_url":"https://doi.org/10.5539/cis.v8n2p1","pdf_url":"http://www.ccsenet.org/journal/index.php/cis/article/download/47278/25533","source":{"id":"https://openalex.org/S2764452479","display_name":"Computer and Information Science","issn_l":"1913-8989","issn":["1913-8989","1913-8997"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322531","host_organization_name":"Canadian Center of Science and Education","host_organization_lineage":["https://openalex.org/P4310322531"],"host_organization_lineage_names":["Canadian Center of Science and Education"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer and Information Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.994.7049","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.994.7049","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ccsenet.org/journal/index.php/cis/article/download/47278/25533/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.5539/cis.v8n2p1","is_oa":true,"landing_page_url":"https://doi.org/10.5539/cis.v8n2p1","pdf_url":"http://www.ccsenet.org/journal/index.php/cis/article/download/47278/25533","source":{"id":"https://openalex.org/S2764452479","display_name":"Computer and Information Science","issn_l":"1913-8989","issn":["1913-8989","1913-8997"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322531","host_organization_name":"Canadian Center of Science and Education","host_organization_lineage":["https://openalex.org/P4310322531"],"host_organization_lineage_names":["Canadian Center of Science and Education"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer and Information Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2776650721","display_name":null,"funder_award_id":"1133101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5509717841","display_name":null,"funder_award_id":"71171189","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G603791882","display_name":null,"funder_award_id":"11331012","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6208999373","display_name":null,"funder_award_id":"XDA06010302","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G632621948","display_name":null,"funder_award_id":"XDA06010302","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G6799592476","display_name":null,"funder_award_id":"1133101","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7079690791","display_name":"N/A","funder_award_id":"6010302","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7876063575","display_name":null,"funder_award_id":"11331012","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G8366184331","display_name":null,"funder_award_id":"2011AA01A102","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8397400608","display_name":null,"funder_award_id":"2011CB706900","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2091480483.pdf","grobid_xml":"https://content.openalex.org/works/W2091480483.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1966258309","https://openalex.org/W1969620795","https://openalex.org/W1985363832","https://openalex.org/W1997593628","https://openalex.org/W2006153182","https://openalex.org/W2022527378","https://openalex.org/W2086260323","https://openalex.org/W2087284990","https://openalex.org/W2088904132","https://openalex.org/W2100699015","https://openalex.org/W2107700597","https://openalex.org/W2138123132","https://openalex.org/W2149285697","https://openalex.org/W2620799147","https://openalex.org/W2735337572","https://openalex.org/W6674977452"],"related_works":["https://openalex.org/W3141113327","https://openalex.org/W2080904092","https://openalex.org/W3035974271","https://openalex.org/W3161514703","https://openalex.org/W3207627914","https://openalex.org/W2270959725","https://openalex.org/W2151525839","https://openalex.org/W648253840","https://openalex.org/W2051329268","https://openalex.org/W2092572272"],"abstract_inverted_index":{"In":[0,66],"the":[1,15,21,30,33,44,48,64,71,105,112,118],"k-splittable":[2,77],"flow":[3,130],"problem,":[4,87],"each":[5,26,97],"commodity":[6,98],"can":[7],"only":[8,106],"use":[9],"at":[10],"most":[11],"k":[12],"paths":[13,24,95],"and":[14,90,104],"key":[16],"point":[17],"is":[18,37,41,50,111,131],"to":[19,53,58],"find":[20],"suitable":[22,127],"transmitting":[23],"for":[25,85,96,133],"commodity.":[27],"To":[28],"guarantee":[29],"efficiency":[31],"of":[32],"network,":[34],"minimizing":[35],"congestion":[36,59],"important,":[38],"but":[39,62],"it":[40],"not":[42,63],"enough,":[43],"cost":[45],"consumed":[46],"by":[47,121],"network":[49],"also":[51],"needed":[52],"minimize.":[54],"Most":[55],"researches":[56],"restrict":[57],"or":[60],"cost,":[61],"both.":[65],"this":[67,86],"paper,":[68],"we":[69],"consider":[70],"bi-objective":[72],"(minimize":[73],"congestion,":[74],"minimize":[75],"cost)":[76],"problem.":[78],"We":[79,116],"propose":[80],"three":[81,119],"different":[82],"heuristic":[83],"algorithms":[84,110,120],"A1,":[88],"A2":[89],"A3.":[91],"Each":[92],"algorithm":[93],"finds":[94],"in":[99],"a":[100],"feasible":[101,114,129],"splittable":[102],"flow,":[103],"difference":[107],"between":[108],"these":[109],"initial":[113,128],"flow.":[115],"compare":[117],"testing":[122],"instances,":[123],"showing":[124],"that":[125],"choosing":[126],"important":[132],"obtaining":[134],"good":[135],"results.":[136]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}