{"id":"https://openalex.org/W2898517553","doi":"https://doi.org/10.1080/03610918.2018.1468459","title":"Linear programming bounds on the union probability","display_name":"Linear programming bounds on the union probability","publication_year":2018,"publication_date":"2018-10-27","ids":{"openalex":"https://openalex.org/W2898517553","doi":"https://doi.org/10.1080/03610918.2018.1468459","mag":"2898517553"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2018.1468459","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2018.1468459","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","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/A5101526256","display_name":"Jun Yang","orcid":"https://orcid.org/0000-0001-7503-3235"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jun Yang","raw_affiliation_strings":["Department of Statistical Sciences, University of Toronto, Toronto, Ontario, Canada;;"],"affiliations":[{"raw_affiliation_string":"Department of Statistical Sciences, University of Toronto, Toronto, Ontario, Canada;;","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065742137","display_name":"Fady Alajaji","orcid":"https://orcid.org/0000-0002-7980-724X"},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Fady Alajaji","raw_affiliation_strings":["Department of Mathematics and Statistics, Queen\u2019s University, Kingston, Ontario, Canada","Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen\u2019s University, Kingston, Ontario, Canada","institution_ids":["https://openalex.org/I204722609"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada","institution_ids":["https://openalex.org/I204722609"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008641491","display_name":"Glen Takahara","orcid":null},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Glen Takahara","raw_affiliation_strings":["Department of Mathematics and Statistics, Queen\u2019s University, Kingston, Ontario, Canada","Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen\u2019s University, Kingston, Ontario, Canada","institution_ids":["https://openalex.org/I204722609"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada","institution_ids":["https://openalex.org/I204722609"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5065742137"],"corresponding_institution_ids":["https://openalex.org/I204722609"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.15207092,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"48","issue":"9","first_page":"2845","last_page":"2854"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10328","display_name":"Supply Chain and Inventory Management","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1404","display_name":"Management Information Systems"},"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9914000034332275,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.7753329873085022},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.6698178052902222},{"id":"https://openalex.org/keywords/event","display_name":"Event (particle physics)","score":0.6264054179191589},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5696060061454773},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.534648597240448},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4434756636619568},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4158196449279785},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3432316780090332},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3141670823097229},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2840425372123718},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.26373419165611267},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05401936173439026}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7753329873085022},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.6698178052902222},{"id":"https://openalex.org/C2779662365","wikidata":"https://www.wikidata.org/wiki/Q5416694","display_name":"Event (particle physics)","level":2,"score":0.6264054179191589},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5696060061454773},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.534648597240448},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4434756636619568},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4158196449279785},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3432316780090332},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3141670823097229},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2840425372123718},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26373419165611267},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05401936173439026},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2018.1468459","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2018.1468459","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5299999713897705,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1945575495","https://openalex.org/W1966387432","https://openalex.org/W1979144155","https://openalex.org/W1982919008","https://openalex.org/W1985131175","https://openalex.org/W2005225596","https://openalex.org/W2021851424","https://openalex.org/W2038950164","https://openalex.org/W2056815865","https://openalex.org/W2072546112","https://openalex.org/W2083533121","https://openalex.org/W2092271237","https://openalex.org/W2098111206","https://openalex.org/W2114713753","https://openalex.org/W2144543987","https://openalex.org/W2155409730","https://openalex.org/W2168925234","https://openalex.org/W2316919907","https://openalex.org/W2327232970","https://openalex.org/W2569664619","https://openalex.org/W2595530668","https://openalex.org/W2963182207"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2487162673","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2942366970","https://openalex.org/W2807634898","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W4360593462"],"abstract_inverted_index":{"Lower":[0],"and":[1,18,44],"upper":[2],"bounds":[3,51,68],"on":[4],"the":[5,16,70],"union":[6],"probability":[7],"for":[8],"N":[9],"events":[10],"are":[11,37,45],"derived":[12],"in":[13,69],"terms":[14],"of":[15],"individual":[17],"pairwise":[19],"event":[20],"probabilities":[21],"by":[22],"solving":[23],"a":[24],"linear":[25],"program":[26],"with":[27,66],"(N\u22121)3+N+32":[28],"variables.":[29],"The":[30],"bounds,":[31],"which":[32,52],"can":[33],"be":[34,40],"efficiently":[35],"determined,":[36],"shown":[38],"to":[39],"optimal":[41,50],"when":[42],"N\u22645":[43],"always":[46],"sharper":[47],"than":[48],"recent":[49],"use":[53],"slightly":[54],"less":[55],"information.":[56],"Their":[57],"competitive":[58],"sharpness":[59],"is":[60],"also":[61],"illustrated":[62],"via":[63],"numerical":[64],"comparisons":[65],"state-of-the-art":[67],"literature.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}