{"id":"https://openalex.org/W4405717895","doi":"https://doi.org/10.1109/tnse.2024.3521224","title":"Time and Energy Costs for Intra-Layer Consensus of Multi-Layer Networks","display_name":"Time and Energy Costs for Intra-Layer Consensus of Multi-Layer Networks","publication_year":2024,"publication_date":"2024-12-23","ids":{"openalex":"https://openalex.org/W4405717895","doi":"https://doi.org/10.1109/tnse.2024.3521224"},"language":"en","primary_location":{"id":"doi:10.1109/tnse.2024.3521224","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2024.3521224","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-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/A5084484072","display_name":"Rong Dan","orcid":"https://orcid.org/0000-0003-4273-921X"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dan Rong","raw_affiliation_strings":["School of Mathematics, China University of Mining and Technology, Xuzhou, China"],"raw_orcid":"https://orcid.org/0000-0003-4273-921X","affiliations":[{"raw_affiliation_string":"School of Mathematics, China University of Mining and Technology, Xuzhou, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035669378","display_name":"Haifeng Dai","orcid":"https://orcid.org/0000-0001-9960-8128"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haifeng Dai","raw_affiliation_strings":["School of Cyber Science and Engineering, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0001-9960-8128","affiliations":[{"raw_affiliation_string":"School of Cyber Science and Engineering, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003822957","display_name":"Yongzheng Sun","orcid":"https://orcid.org/0000-0001-9504-5663"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongzheng Sun","raw_affiliation_strings":["School of Mathematics and the Shenzhen Research Institute, China University of Mining and Technology, Xuzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-9504-5663","affiliations":[{"raw_affiliation_string":"School of Mathematics and the Shenzhen Research Institute, China University of Mining and Technology, Xuzhou, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040088510","display_name":"Guanghui Wen","orcid":"https://orcid.org/0000-0003-0070-8597"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guanghui Wen","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-0070-8597","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9366,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.78283541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"12","issue":"2","first_page":"900","last_page":"910"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","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/T10249","display_name":"Distributed Control Multi-Agent Systems","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/T10080","display_name":"Energy Efficient Wireless Sensor Networks","score":0.9988999962806702,"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/T13052","display_name":"Molecular Communication and Nanonetworks","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/layer","display_name":"Layer (electronics)","score":0.6288517713546753},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5511497855186462},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.3911292850971222},{"id":"https://openalex.org/keywords/distributed-computing","display_name":"Distributed computing","score":0.33679699897766113},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.20898637175559998},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.12400877475738525}],"concepts":[{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.6288517713546753},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5511497855186462},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.3911292850971222},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.33679699897766113},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.20898637175559998},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.12400877475738525}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tnse.2024.3521224","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnse.2024.3521224","pdf_url":null,"source":{"id":"https://openalex.org/S2484352698","display_name":"IEEE Transactions on Network Science and Engineering","issn_l":"2327-4697","issn":["2327-4697","2334-329X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Network Science and Engineering","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8500000238418579}],"awards":[{"id":"https://openalex.org/G2575069074","display_name":null,"funder_award_id":"62088101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2843151570","display_name":null,"funder_award_id":"62325304","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G334372649","display_name":null,"funder_award_id":"2019T120476","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G3545465040","display_name":null,"funder_award_id":"BK20211241","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G6971051528","display_name":null,"funder_award_id":"12271519","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8516247378","display_name":null,"funder_award_id":"2017M621860","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G8967878662","display_name":null,"funder_award_id":"U22B2046","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1970811568","https://openalex.org/W2005525403","https://openalex.org/W2068801139","https://openalex.org/W2070722739","https://openalex.org/W2079973473","https://openalex.org/W2082868669","https://openalex.org/W2083787309","https://openalex.org/W2099175737","https://openalex.org/W2104109956","https://openalex.org/W2107396783","https://openalex.org/W2109987654","https://openalex.org/W2131164291","https://openalex.org/W2154414031","https://openalex.org/W2164928285","https://openalex.org/W2172143163","https://openalex.org/W2200614381","https://openalex.org/W2460773313","https://openalex.org/W2609122333","https://openalex.org/W2610328900","https://openalex.org/W2767959255","https://openalex.org/W2768800310","https://openalex.org/W2890240334","https://openalex.org/W2897884201","https://openalex.org/W2948868795","https://openalex.org/W2962871354","https://openalex.org/W2997361925","https://openalex.org/W3006517080","https://openalex.org/W3036322696","https://openalex.org/W3036953780","https://openalex.org/W3037683188","https://openalex.org/W3049752772","https://openalex.org/W3095812073","https://openalex.org/W3102573360","https://openalex.org/W3106041418","https://openalex.org/W3107156000","https://openalex.org/W3125908070","https://openalex.org/W3168895612","https://openalex.org/W3191642774","https://openalex.org/W3199485405","https://openalex.org/W4210580591","https://openalex.org/W4220916075","https://openalex.org/W4221108782","https://openalex.org/W4233082427","https://openalex.org/W4293143260","https://openalex.org/W4321195190","https://openalex.org/W4362640737","https://openalex.org/W4389215222","https://openalex.org/W4390904867"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Multi-layer":[0],"network":[1,23,73],"representation":[2],"has":[3,12],"been":[4],"shown":[5],"to":[6,41,92,105,125],"well":[7],"characterize":[8],"real":[9],"networks,":[10,66],"and":[11,28,112],"revealed":[13],"some":[14],"potential":[15],"phenomenon":[16],"beyond":[17],"the":[18,43,53,72,86,100,127],"interpretation":[19],"ability":[20],"of":[21,56,94],"single-layer":[22],"successfully.":[24],"Despite":[25],"its":[26],"uniqueness":[27],"excitement,":[29],"intra-layer":[30,45],"consensus":[31,46,58,117],"gets":[32],"less":[33],"attention.":[34],"This":[35],"paper":[36],"proposes":[37],"a":[38,67,75,82],"discontinuous":[39,83],"protocol":[40],"address":[42],"finite-time":[44,57],"problem":[47],"for":[48,115],"multi-layer":[49],"networks.":[50],"Different":[51],"from":[52],"traditional":[54],"results":[55],"schemes":[59],"work":[60],"only":[61],"on":[62],"undirected":[63],"or":[64,97],"detail-balanced":[65],"more":[68],"general":[69],"case":[70],"that":[71],"contains":[74],"directed":[76],"spanning":[77],"tree":[78],"is":[79,103,123],"considered":[80],"with":[81],"protocol.":[84],"On":[85],"other":[87],"hand,":[88],"without":[89],"limiting":[90],"networks":[91],"be":[93,106],"drive-response":[95],"type":[96],"specifically":[98],"duplexed,":[99],"inter-layer":[101],"topology":[102],"assumed":[104],"unidirectional.":[107],"In":[108],"addition,":[109],"both":[110],"time":[111],"energy":[113],"costs":[114],"achieving":[116],"are":[118],"studied.":[119],"Finally,":[120],"an":[121],"example":[122],"given":[124],"verify":[126],"theoretical":[128],"results.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}