{"id":"https://openalex.org/W2924421263","doi":"https://doi.org/10.1155/2019/4561845","title":"Efficient Enumeration of <i>d</i>\u2010Minimal Paths in Reliability Evaluation of Multistate Networks","display_name":"Efficient Enumeration of <i>d</i>\u2010Minimal Paths in Reliability Evaluation of Multistate Networks","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2924421263","doi":"https://doi.org/10.1155/2019/4561845","mag":"2924421263"},"language":"en","primary_location":{"id":"doi:10.1155/2019/4561845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4561845","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4561845.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/4561845.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101988902","display_name":"Xiu-Zhen Xu","orcid":"https://orcid.org/0000-0002-8618-9566"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]},{"id":"https://openalex.org/I4210166499","display_name":"Henan Polytechnic University","ror":"https://ror.org/05vr1c885","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166499"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiu-Zhen Xu","raw_affiliation_strings":["School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China","School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000","School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065"],"raw_orcid":"https://orcid.org/0000-0002-8618-9566","affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China","institution_ids":["https://openalex.org/I4210166499"]},{"raw_affiliation_string":"School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","institution_ids":["https://openalex.org/I10535382"]},{"raw_affiliation_string":"School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000","institution_ids":["https://openalex.org/I4210166499"]},{"raw_affiliation_string":"School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088158018","display_name":"Yi-Feng Niu","orcid":"https://orcid.org/0000-0002-7246-8089"},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yi-Feng Niu","raw_affiliation_strings":["School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065"],"raw_orcid":"https://orcid.org/0000-0002-7246-8089","affiliations":[{"raw_affiliation_string":"School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065, China","institution_ids":["https://openalex.org/I10535382"]},{"raw_affiliation_string":"School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing 400065","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100703198","display_name":"Qing Li","orcid":"https://orcid.org/0000-0002-6202-4441"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qing Li","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590"],"raw_orcid":"https://orcid.org/0000-0002-6202-4441","affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]},{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590","institution_ids":["https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088158018"],"corresponding_institution_ids":["https://openalex.org/I10535382"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":1.1166,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.76600087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"2019","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T11357","display_name":"Risk and Safety Analysis","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12423","display_name":"Software Reliability and Analysis Research","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/enumeration","display_name":"Enumeration","score":0.46755707263946533},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.4368855059146881},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.423500657081604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35128653049468994},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28579360246658325},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.26242703199386597},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07909318804740906}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.46755707263946533},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.4368855059146881},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.423500657081604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35128653049468994},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28579360246658325},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26242703199386597},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07909318804740906},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2019/4561845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4561845","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4561845.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c52f017e86dd49d7974b7fd6263eca26","is_oa":true,"landing_page_url":"https://doaj.org/article/c52f017e86dd49d7974b7fd6263eca26","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/4561845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/4561845","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/4561845.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4481394672","display_name":"\u9053\u8def\u4ea4\u901a\u7f51\u7edc\u9000\u5316\u901a\u884c\u80fd\u529b\u53ca\u5176\u53ef\u9760\u6027\u7814\u7a76","funder_award_id":"71601072","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G464663253","display_name":"\u5927\u6570\u636e\u73af\u5883\u4e0b\u53cc\u8fb9\u611f\u77e5\u7684\u4e3b\u52a8\u670d\u52a1\u805a\u5408\u7406\u8bba\u4e0e\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61872126","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G794676824","display_name":null,"funder_award_id":"7160107","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8520207986","display_name":null,"funder_award_id":"172102310677","funder_id":"https://openalex.org/F4320327051","funder_display_name":"Science and Technology Department of Henan Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327051","display_name":"Science and Technology Department of Henan Province","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2924421263.pdf","grobid_xml":"https://content.openalex.org/works/W2924421263.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W317510280","https://openalex.org/W1938707398","https://openalex.org/W1968404775","https://openalex.org/W1971863084","https://openalex.org/W1981179503","https://openalex.org/W1985342141","https://openalex.org/W1993050408","https://openalex.org/W1993210728","https://openalex.org/W1997275614","https://openalex.org/W2003287485","https://openalex.org/W2004132136","https://openalex.org/W2049401020","https://openalex.org/W2051022544","https://openalex.org/W2064881562","https://openalex.org/W2092314182","https://openalex.org/W2109998235","https://openalex.org/W2124000105","https://openalex.org/W2144173369","https://openalex.org/W2167947550","https://openalex.org/W2169845564","https://openalex.org/W2243394267","https://openalex.org/W2336768207","https://openalex.org/W2418160670","https://openalex.org/W2419250400","https://openalex.org/W2552896552","https://openalex.org/W2589305619","https://openalex.org/W2611246976","https://openalex.org/W2754699040","https://openalex.org/W2789850002","https://openalex.org/W2790252527","https://openalex.org/W2793224838","https://openalex.org/W2890624544","https://openalex.org/W2891203478","https://openalex.org/W2891352884","https://openalex.org/W2901317875","https://openalex.org/W4213060235","https://openalex.org/W4244424643"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W108845024","https://openalex.org/W2406961474","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2952598754","https://openalex.org/W3042106073","https://openalex.org/W2143566611","https://openalex.org/W4251460363"],"abstract_inverted_index":{"A":[0,15],"number":[1],"of":[2,19,38,82,97,193],"real\u2010world":[3],"complex":[4],"networks":[5,11],"can":[6,151],"be":[7,113,152],"modeled":[8],"as":[9,89,154,156],"multistate":[10,16,20,58],"for":[12,57,107,131],"performance":[13,26],"analysis.":[14],"network":[17,40,59,186,194],"consists":[18],"components":[21],"and":[22,101,104,123,160],"possesses":[23],"multiple":[24],"different":[25],"levels.":[27],"For":[28],"such":[29,146],"a":[30,48,79,92,102,108,179],"network,":[31],"reliability":[32,60],"is":[33,62,86,117,141,168,187],"concerned":[34],"with":[35],"the":[36,39,120,124,136,148,165,191],"probability":[37],"capacity":[41],"level":[42,51],"greater":[43],"than":[44],"or":[45],"equal":[46],"to":[47,73,90,112,129,183,189],"predetermined":[49],"demand":[50],"d":[52,64,75,98,114,132,174],".":[53],"One":[54],"major":[55],"method":[56],"evaluation":[61],"using":[63],"\u2010minimal":[65,76,99,115,133,175],"paths.":[66,77,176],"This":[67],"paper":[68],"proposes":[69],"an":[70],"efficient":[71,170],"algorithm":[72,122,126,167],"find":[74],"First,":[78],"new":[80],"concept":[81],"qualified":[83,109],"state":[84,110],"vector":[85,111],"defined":[87],"so":[88],"fix":[91],"relatively":[93],"smaller":[94],"search":[95,130,138],"space":[96,139],"paths,":[100],"sufficient":[103],"necessary":[105],"condition":[106],"path":[116],"established.":[118],"Then,":[119],"max\u2010flow":[121],"enumeration":[125],"are":[127],"integrated":[128],"paths":[134],"in":[135,171],"determined":[137],"that":[140,147,164],"recursively":[142],"divided":[143],"into":[144],"subspaces":[145],"searching":[149],"efficiency":[150],"increased":[153],"much":[155],"possible.":[157],"Both":[158],"analytical":[159],"numerical":[161],"results":[162],"show":[163],"proposed":[166],"more":[169],"finding":[172],"all":[173],"In":[177],"addition,":[178],"case":[180],"study":[181],"related":[182],"power":[184],"transmission":[185],"performed":[188],"demonstrate":[190],"implication":[192],"reliability.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":5}],"updated_date":"2026-06-06T09:05:17.133730","created_date":"2019-04-01T00:00:00"}