{"id":"https://openalex.org/W2033350906","doi":"https://doi.org/10.1002/net.3230210306","title":"Reliability covering problems","display_name":"Reliability covering problems","publication_year":1991,"publication_date":"1991-05-01","ids":{"openalex":"https://openalex.org/W2033350906","doi":"https://doi.org/10.1002/net.3230210306","mag":"2033350906"},"language":"en","primary_location":{"id":"doi:10.1002/net.3230210306","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230210306","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","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/A5035102045","display_name":"Michael O. Ball","orcid":"https://orcid.org/0000-0003-2757-8569"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. O. Ball","raw_affiliation_strings":["College of Business and Management, University of Maryland, College Park, Maryland 20742","College of Business and Management, University of Maryland, College Park, Maryland, 20742"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Business and Management, University of Maryland, College Park, Maryland 20742","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"College of Business and Management, University of Maryland, College Park, Maryland, 20742","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005781105","display_name":"J. Scott Provan","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. S. Provan","raw_affiliation_strings":["Department of Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599","Department of Operations Research, University  of North Carolina, Chapel Hill, North Carolina 27599"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"Department of Operations Research, University  of North Carolina, Chapel Hill, North Carolina 27599","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064088962","display_name":"Douglas R. Shier","orcid":"https://orcid.org/0000-0002-7972-7637"},"institutions":[{"id":"https://openalex.org/I16285277","display_name":"William & Mary","ror":"https://ror.org/03hsf0573","country_code":"US","type":"education","lineage":["https://openalex.org/I16285277"]},{"id":"https://openalex.org/I267592682","display_name":"Williams (United States)","ror":"https://ror.org/007zhvp17","country_code":"US","type":"company","lineage":["https://openalex.org/I267592682"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. R. Shier","raw_affiliation_strings":["Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23185","Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23185"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23185","institution_ids":["https://openalex.org/I16285277","https://openalex.org/I267592682"]},{"raw_affiliation_string":"Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23185","institution_ids":["https://openalex.org/I16285277","https://openalex.org/I267592682"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":3.4063,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.90345173,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"21","issue":"3","first_page":"345","last_page":"357"},"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/T12423","display_name":"Software Reliability and Analysis Research","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9983000159263611,"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/reliability","display_name":"Reliability (semiconductor)","score":0.7472556829452515},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6551841497421265},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5613042712211609},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.467821329832077},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4528809189796448},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.41118499636650085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3979004919528961},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37253934144973755},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29562079906463623}],"concepts":[{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.7472556829452515},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6551841497421265},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5613042712211609},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.467821329832077},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4528809189796448},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.41118499636650085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3979004919528961},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37253934144973755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29562079906463623},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.3230210306","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.3230210306","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W587622775","https://openalex.org/W1551599350","https://openalex.org/W1964692111","https://openalex.org/W1991536882","https://openalex.org/W2011039300","https://openalex.org/W2034315530","https://openalex.org/W2067903128","https://openalex.org/W2087555137","https://openalex.org/W2115826669","https://openalex.org/W2125690626","https://openalex.org/W2156478854","https://openalex.org/W2161184219","https://openalex.org/W2169621137"],"related_works":["https://openalex.org/W2046435967","https://openalex.org/W4231775656","https://openalex.org/W2980963558","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"studies":[3],"the":[4,23,34,77,84,108],"reliability":[5,97],"covering":[6],"problem,":[7],"in":[8],"which":[9],"given":[10],"routes":[11,24,56,78,85],"provides":[12],"service":[13],"to":[14,27,32,61,110],"various":[15],"stops":[16,38],"(e.g.,":[17],"of":[18,79,89],"a":[19,80,90],"transit":[20],"system).":[21],"If":[22],"are":[25,57,68,86],"subject":[26],"failure,":[28],"it":[29],"is":[30,47,52,74],"desired":[31],"find":[33],"probability":[35],"that":[36,49],"all":[37],"will":[39],"be":[40],"covered":[41],"by":[42,115,118],"an":[43,62],"operating":[44],"route.":[45],"It":[46],"shown":[48],"this":[50],"problem":[51],"NP\u2010hard":[53],"even":[54],"when":[55,70,83],"defined":[58],"with":[59],"respect":[60],"underlying":[63],"tree.":[64,93],"Polynomially":[65],"solvable":[66],"cases":[67,95],"developed":[69],"some":[71],"additional":[72],"structure":[73],"imposed":[75],"on":[76],"tree:":[81],"e.g.,":[82],"directed":[87,92],"paths":[88],"rooted":[91],"These":[94],"generalize":[96],"computations":[98],"for":[99],"consecutive":[100],"k":[101],"\u2010out\u2010of\u2010":[102],"n":[103],"systems":[104,113],"as":[105,107],"well":[106],"extensions":[109],"consecutively":[111],"connected":[112],"studied":[114],"Shanthikumar":[116],"and":[117,120],"Hwang":[119],"Yao.":[121]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}