{"id":"https://openalex.org/W2969917739","doi":"https://doi.org/10.1155/2019/9520324","title":"On the Location of a Constrained <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mi>k</mml:mi><mml:mo>-</mml:mo></mml:math>Tree Facility in a Tree Network with Unreliable Edges","display_name":"On the Location of a Constrained <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"><mml:mi>k</mml:mi><mml:mo>-</mml:mo></mml:math>Tree Facility in a Tree Network with Unreliable Edges","publication_year":2019,"publication_date":"2019-08-21","ids":{"openalex":"https://openalex.org/W2969917739","doi":"https://doi.org/10.1155/2019/9520324","mag":"2969917739"},"language":"en","primary_location":{"id":"doi:10.1155/2019/9520324","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9520324","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/9520324.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","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/jam/2019/9520324.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084524478","display_name":"Abdallah W. Aboutahoun","orcid":"https://orcid.org/0000-0001-7977-3425"},"institutions":[{"id":"https://openalex.org/I4210150948","display_name":"Zewail City of Science and Technology","ror":"https://ror.org/04w5f4y88","country_code":"EG","type":"education","lineage":["https://openalex.org/I4210150948"]},{"id":"https://openalex.org/I84524832","display_name":"Alexandria University","ror":"https://ror.org/00mzz1w90","country_code":"EG","type":"education","lineage":["https://openalex.org/I84524832"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Abdallah W. Aboutahoun","raw_affiliation_strings":["Applied Mathematics and Information Science Department, Zewail City of Science and Technology, 6th of October City, Giza, Egypt","Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt"],"raw_orcid":"https://orcid.org/0000-0001-7977-3425","affiliations":[{"raw_affiliation_string":"Applied Mathematics and Information Science Department, Zewail City of Science and Technology, 6th of October City, Giza, Egypt","institution_ids":["https://openalex.org/I4210150948"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt","institution_ids":["https://openalex.org/I84524832"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017576234","display_name":"Eman Fares","orcid":"https://orcid.org/0000-0002-3362-3998"},"institutions":[{"id":"https://openalex.org/I146977602","display_name":"Pharos University in Alexandria","ror":"https://ror.org/04cgmbd24","country_code":"EG","type":"education","lineage":["https://openalex.org/I146977602"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Eman Fares","raw_affiliation_strings":["Department of Basic Sciences, Faculty of Engineering, Pharos University, Alexandria, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Faculty of Engineering, Pharos University, Alexandria, Egypt","institution_ids":["https://openalex.org/I146977602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084524478"],"corresponding_institution_ids":["https://openalex.org/I4210150948","https://openalex.org/I84524832"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13771514,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2019","issue":null,"first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9919000267982483,"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"}},{"id":"https://openalex.org/T11500","display_name":"Evacuation and Crowd Dynamics","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/algorithm","display_name":"Algorithm","score":0.7080718278884888},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5511785745620728},{"id":"https://openalex.org/keywords/database","display_name":"Database","score":0.36807602643966675},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36803585290908813},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3639596700668335}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7080718278884888},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5511785745620728},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.36807602643966675},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36803585290908813},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3639596700668335}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/9520324","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9520324","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/9520324.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1568858741","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1568858741","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:9ed6dba6d5d94b6cb3414593249d2c45","is_oa":true,"landing_page_url":"https://doaj.org/article/9ed6dba6d5d94b6cb3414593249d2c45","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":"Journal of Applied Mathematics, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/9520324","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/9520324","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/9520324.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2969917739.pdf","grobid_xml":"https://content.openalex.org/works/W2969917739.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1968685726","https://openalex.org/W1991466654","https://openalex.org/W1994798705","https://openalex.org/W1996969231","https://openalex.org/W1999753357","https://openalex.org/W2001395951","https://openalex.org/W2002665837","https://openalex.org/W2008250711","https://openalex.org/W2025403762","https://openalex.org/W2026839440","https://openalex.org/W2037362003","https://openalex.org/W2060989264","https://openalex.org/W2061620935","https://openalex.org/W2064072796","https://openalex.org/W2081344300","https://openalex.org/W2085637279","https://openalex.org/W2092866803","https://openalex.org/W2093467530","https://openalex.org/W2119252805","https://openalex.org/W2129084394","https://openalex.org/W2157047836","https://openalex.org/W2165767919","https://openalex.org/W4240586972","https://openalex.org/W4243837074"],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W3046775127","https://openalex.org/W4394896187","https://openalex.org/W3170094116","https://openalex.org/W4386462264","https://openalex.org/W3107602296","https://openalex.org/W4364306694","https://openalex.org/W4312192474","https://openalex.org/W4283697347"],"abstract_inverted_index":{"Given":[0],"a":[1,29,35,47,91,94,105,131],"tree":[2,139],"network":[3,100,109,117],"<mml:math":[4,8,41,52,133,142,155],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,9,42,53,134,143,156],"id=\"M2\"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math>":[6],"with":[7,39,46],"id=\"M3\"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>":[10],"vertices":[11],"where":[12],"each":[13],"edge":[14],"has":[15],"an":[16],"independent":[17],"operational":[18,70],"probability,":[19],"we":[20],"are":[21,63,160],"interested":[22],"in":[23,34,101],"finding":[24,130],"the":[25,57,66,82,99,113,120,124,151,164,167],"optimal":[26],"location":[27,92],"of":[28,37,49,60,85,93,116,141,150,166],"reliable":[30,79,95,132],"service":[31,75],"provider":[32],"facility":[33,97],"shape":[36],"subtree":[38,68],"exactly":[40],"id=\"M4\"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>":[43],"leaves":[44],"and":[45,123],"diameter":[48],"at":[50,77],"most":[51],"id=\"M5\"><mml:mrow><mml:mi>l</mml:mi></mml:mrow></mml:math>":[54],"which":[55],"maximizes":[56],"expected":[58],"number":[59],"nodes":[61,122],"that":[62],"reachable":[64],"from":[65],"selected":[67],"by":[69,111],"paths.":[71],"Demand":[72],"requests":[73],"for":[74,129],"originate":[76],"perfectly":[78],"nodes.":[80],"So,":[81],"major":[83],"concern":[84],"this":[86],"paper":[87],"is":[88,145,154],"to":[89,103,108,162],"find":[90],"tree-shaped":[96],"on":[98],"order":[102],"provide":[104],"maximum":[106],"access":[107],"services":[110],"ensuring":[112],"highest":[114],"level":[115],"connectivity":[118],"between":[119],"demand":[121],"facility.":[125],"An":[126],"efficient":[127],"algorithm":[128,153],"id=\"M6\"><mml:mo":[135],"stretchy=\"false\">(</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi><mml:mo":[136],"stretchy=\"false\">)</mml:mo></mml:math>":[137],"\u2013":[138],"core":[140],"id=\"M7\"><mml:mrow><mml:mi>T</mml:mi></mml:mrow></mml:math>":[144],"developed.":[146],"The":[147],"time":[148],"complexity":[149],"proposed":[152,168],"id=\"M8\"><mml:mi>O</mml:mi><mml:mfenced":[157],"separators=\"|\"><mml:mrow><mml:mi>l</mml:mi><mml:mi>k</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:math>":[158],"Examples":[159],"provided":[161],"illustrate":[163],"performance":[165],"algorithm.":[169]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}