{"id":"https://openalex.org/W4363673420","doi":"https://doi.org/10.3390/computation11040074","title":"Modification of the Bellman\u2013Ford Algorithm for Finding the Optimal Route in Multilayer Network Structures","display_name":"Modification of the Bellman\u2013Ford Algorithm for Finding the Optimal Route in Multilayer Network Structures","publication_year":2023,"publication_date":"2023-04-07","ids":{"openalex":"https://openalex.org/W4363673420","doi":"https://doi.org/10.3390/computation11040074"},"language":"en","primary_location":{"id":"doi:10.3390/computation11040074","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11040074","pdf_url":"https://www.mdpi.com/2079-3197/11/4/74/pdf?version=1680863047","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/11/4/74/pdf?version=1680863047","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027154818","display_name":"\u041e. \u041f. \u0422\u0438\u043c\u043e\u0444\u0435\u0435\u0432\u0430","orcid":"https://orcid.org/0000-0002-1935-7697"},"institutions":[{"id":"https://openalex.org/I4210138365","display_name":"Nizhny Novgorod State Technical University","ror":"https://ror.org/037d0vf92","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210138365"]},{"id":"https://openalex.org/I47410878","display_name":"Nizhny Novgorod State Pedagogical University","ror":"https://ror.org/05mm0yv21","country_code":"RU","type":"education","lineage":["https://openalex.org/I47410878"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Olga Timofeeva","raw_affiliation_strings":["Department of Informatics and Control Systems, Nizhny Novgorod State Technical University, R.E. Alekseeva, 603950 Nizhny Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Informatics and Control Systems, Nizhny Novgorod State Technical University, R.E. Alekseeva, 603950 Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I47410878","https://openalex.org/I4210138365"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012522711","display_name":"Alexey Sannikov","orcid":null},"institutions":[{"id":"https://openalex.org/I4210138365","display_name":"Nizhny Novgorod State Technical University","ror":"https://ror.org/037d0vf92","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210138365"]},{"id":"https://openalex.org/I47410878","display_name":"Nizhny Novgorod State Pedagogical University","ror":"https://ror.org/05mm0yv21","country_code":"RU","type":"education","lineage":["https://openalex.org/I47410878"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexey Sannikov","raw_affiliation_strings":["Department of Informatics and Control Systems, Nizhny Novgorod State Technical University, R.E. Alekseeva, 603950 Nizhny Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Informatics and Control Systems, Nizhny Novgorod State Technical University, R.E. Alekseeva, 603950 Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I47410878","https://openalex.org/I4210138365"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005033545","display_name":"Maria Stepanenko","orcid":null},"institutions":[{"id":"https://openalex.org/I4210138365","display_name":"Nizhny Novgorod State Technical University","ror":"https://ror.org/037d0vf92","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210138365"]},{"id":"https://openalex.org/I47410878","display_name":"Nizhny Novgorod State Pedagogical University","ror":"https://ror.org/05mm0yv21","country_code":"RU","type":"education","lineage":["https://openalex.org/I47410878"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Maria Stepanenko","raw_affiliation_strings":["Department of Informatics and Control Systems, Nizhny Novgorod State Technical University, R.E. Alekseeva, 603950 Nizhny Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Informatics and Control Systems, Nizhny Novgorod State Technical University, R.E. Alekseeva, 603950 Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I47410878","https://openalex.org/I4210138365"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049539741","display_name":"T.I. Balashova","orcid":"https://orcid.org/0000-0002-1328-3228"},"institutions":[{"id":"https://openalex.org/I4210138365","display_name":"Nizhny Novgorod State Technical University","ror":"https://ror.org/037d0vf92","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210138365"]},{"id":"https://openalex.org/I47410878","display_name":"Nizhny Novgorod State Pedagogical University","ror":"https://ror.org/05mm0yv21","country_code":"RU","type":"education","lineage":["https://openalex.org/I47410878"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Tatiana Balashova","raw_affiliation_strings":["Department of Informatics and Control Systems, Nizhny Novgorod State Technical University, R.E. Alekseeva, 603950 Nizhny Novgorod, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Informatics and Control Systems, Nizhny Novgorod State Technical University, R.E. Alekseeva, 603950 Nizhny Novgorod, Russia","institution_ids":["https://openalex.org/I47410878","https://openalex.org/I4210138365"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5027154818"],"corresponding_institution_ids":["https://openalex.org/I4210138365","https://openalex.org/I47410878"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.4641,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.58619271,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":"4","first_page":"74","last_page":"74"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13527","display_name":"Transportation Systems and Logistics","score":0.9523000121116638,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T13527","display_name":"Transportation Systems and Logistics","score":0.9523000121116638,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T13181","display_name":"Economic and Technological Systems Analysis","score":0.9448000192642212,"subfield":{"id":"https://openalex.org/subfields/1405","display_name":"Management of Technology and Innovation"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7294459939002991},{"id":"https://openalex.org/keywords/problem-statement","display_name":"Problem statement","score":0.5975947976112366},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5624691843986511},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5458046793937683},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.5082442164421082},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4961172044277191},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.417097806930542},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3455127477645874},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.20779812335968018},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.12946075201034546},{"id":"https://openalex.org/keywords/management-science","display_name":"Management science","score":0.10652098059654236},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09719446301460266}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7294459939002991},{"id":"https://openalex.org/C202532154","wikidata":"https://www.wikidata.org/wiki/Q4374193","display_name":"Problem statement","level":2,"score":0.5975947976112366},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5624691843986511},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5458046793937683},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.5082442164421082},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4961172044277191},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.417097806930542},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3455127477645874},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.20779812335968018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.12946075201034546},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.10652098059654236},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09719446301460266},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/computation11040074","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11040074","pdf_url":"https://www.mdpi.com/2079-3197/11/4/74/pdf?version=1680863047","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6ad76062b8ab4c35bc8640a882737ed1","is_oa":true,"landing_page_url":"https://doaj.org/article/6ad76062b8ab4c35bc8640a882737ed1","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 11, Iss 4, p 74 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2079-3197/11/4/74/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/computation11040074","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation; Volume 11; Issue 4; Pages: 74","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/computation11040074","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation11040074","pdf_url":"https://www.mdpi.com/2079-3197/11/4/74/pdf?version=1680863047","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6499999761581421,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4363673420.pdf"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1971035983","https://openalex.org/W2003345268","https://openalex.org/W2901450733","https://openalex.org/W2909085420","https://openalex.org/W3021306889","https://openalex.org/W3103935555","https://openalex.org/W3138951338","https://openalex.org/W3167910853","https://openalex.org/W4245608944","https://openalex.org/W4302011127","https://openalex.org/W4311422840","https://openalex.org/W4313197848","https://openalex.org/W6651190561","https://openalex.org/W6682399607","https://openalex.org/W6713010797"],"related_works":["https://openalex.org/W1981421090","https://openalex.org/W3158538495","https://openalex.org/W2045815042","https://openalex.org/W2092226129","https://openalex.org/W2913619905","https://openalex.org/W4230021867","https://openalex.org/W3125758369","https://openalex.org/W2375898439","https://openalex.org/W2028287801","https://openalex.org/W2069382761"],"abstract_inverted_index":{"One":[0],"of":[1,5,26,47,67,71,88,103,118,125,128,135,144,177,191],"the":[2,6,11,24,27,31,36,45,49,68,96,104,123,126,129,133,145,175],"actual":[3],"tasks":[4],"contemporary":[7],"logistics":[8,155,170],"business":[9],"using":[10,140],"\u201cjust":[12],"in":[13,30,52,150,153,165,169,174,184],"time\u201d":[14],"supply":[15],"planning":[16],"concept,":[17],"is":[18,42,65,75,92],"to":[19,44],"distribute":[20],"manufactured":[21],"goods":[22],"among":[23],"objects":[25],"distribution":[28],"network":[29,53],"most":[32],"efficient":[33],"manner":[34],"at":[35],"lowest":[37],"possible":[38,69],"cost.":[39],"The":[40,55,90,159],"article":[41],"devoted":[43],"problem":[46,56,91],"finding":[48],"optimal":[50],"path":[51],"structures.":[54,194],"statement":[57],"for":[58,139,148],"multilayer":[59,192],"data":[60],"transmission":[61],"networks":[62,156,171],"(MDTN),":[63],"which":[64],"one":[66],"representations":[70],"multimodal":[72],"transport":[73],"networks,":[74,180],"considered.":[76],"Thus,":[77],"each":[78],"MDTN":[79],"layer":[80],"can":[81,162],"be":[82,163],"represented":[83],"as":[84,181,183],"a":[85,110,141],"separate":[86],"type":[87],"transport.":[89],"solved":[93],"by":[94],"modifying":[95],"Bellman\u2013Ford":[97,146],"mathematical":[98],"programming":[99],"algorithm.":[100],"Load":[101],"testing":[102],"modified":[105,142],"method":[106],"was":[107,113],"performed,":[108],"and":[109,120],"comparative":[111,136],"analysis":[112],"given,":[114],"including":[115],"an":[116],"assessment":[117],"speed":[119],"performance,":[121],"proving":[122],"effectiveness":[124],"results":[127,134,160],"study.":[130],"Based":[131],"on":[132],"analysis,":[137],"recommendations":[138],"version":[143],"algorithm":[147],"application":[149],"practical":[151],"problems":[152],"optimizing":[154],"are":[157],"proposed.":[158],"obtained":[161],"used":[164],"practice":[166],"not":[167],"only":[168],"but":[172],"also":[173],"construction":[176],"smart":[178],"energy":[179],"well":[182],"other":[185],"subject":[186],"areas":[187],"that":[188],"require":[189],"optimization":[190],"graph":[193]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2023-04-11T00:00:00"}
