{"id":"https://openalex.org/W7161634753","doi":"https://doi.org/10.1016/j.array.2026.100897","title":"Examination seating optimization using graph coloring and combinatorial design","display_name":"Examination seating optimization using graph coloring and combinatorial design","publication_year":2026,"publication_date":"2026-05-19","ids":{"openalex":"https://openalex.org/W7161634753","doi":"https://doi.org/10.1016/j.array.2026.100897"},"language":"en","primary_location":{"id":"doi:10.1016/j.array.2026.100897","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.array.2026.100897","pdf_url":null,"source":{"id":"https://openalex.org/S4210194039","display_name":"Array","issn_l":"2590-0056","issn":["2590-0056"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Array","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1016/j.array.2026.100897","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Isack E. Kibona","orcid":"https://orcid.org/0000-0003-0479-5173"},"institutions":[{"id":"https://openalex.org/I3129830433","display_name":"Mbeya University of Science and Technology","ror":"https://ror.org/055326464","country_code":"TZ","type":"education","lineage":["https://openalex.org/I3129830433"]}],"countries":["TZ"],"is_corresponding":true,"raw_author_name":"Isack E. Kibona","raw_affiliation_strings":["Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania"],"raw_orcid":"https://orcid.org/0000-0003-0479-5173","affiliations":[{"raw_affiliation_string":"Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania","institution_ids":["https://openalex.org/I3129830433"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jeremiah January","orcid":null},"institutions":[{"id":"https://openalex.org/I3129830433","display_name":"Mbeya University of Science and Technology","ror":"https://ror.org/055326464","country_code":"TZ","type":"education","lineage":["https://openalex.org/I3129830433"]}],"countries":["TZ"],"is_corresponding":false,"raw_author_name":"Jeremiah January","raw_affiliation_strings":["Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania","institution_ids":["https://openalex.org/I3129830433"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Hadija Matimbwa","orcid":null},"institutions":[{"id":"https://openalex.org/I3129830433","display_name":"Mbeya University of Science and Technology","ror":"https://ror.org/055326464","country_code":"TZ","type":"education","lineage":["https://openalex.org/I3129830433"]}],"countries":["TZ"],"is_corresponding":false,"raw_author_name":"Hadija Matimbwa","raw_affiliation_strings":["Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania","institution_ids":["https://openalex.org/I3129830433"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Edwin Nchia","orcid":null},"institutions":[{"id":"https://openalex.org/I3129830433","display_name":"Mbeya University of Science and Technology","ror":"https://ror.org/055326464","country_code":"TZ","type":"education","lineage":["https://openalex.org/I3129830433"]}],"countries":["TZ"],"is_corresponding":false,"raw_author_name":"Edwin Nchia","raw_affiliation_strings":["Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania","institution_ids":["https://openalex.org/I3129830433"]}]},{"author_position":"middle","author":{"id":null,"display_name":"William Matungwa","orcid":null},"institutions":[{"id":"https://openalex.org/I3129830433","display_name":"Mbeya University of Science and Technology","ror":"https://ror.org/055326464","country_code":"TZ","type":"education","lineage":["https://openalex.org/I3129830433"]}],"countries":["TZ"],"is_corresponding":false,"raw_author_name":"William Matungwa","raw_affiliation_strings":["Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania","institution_ids":["https://openalex.org/I3129830433"]}]},{"author_position":"last","author":{"id":null,"display_name":"Said A.H. Vuai","orcid":null},"institutions":[{"id":"https://openalex.org/I3129830433","display_name":"Mbeya University of Science and Technology","ror":"https://ror.org/055326464","country_code":"TZ","type":"education","lineage":["https://openalex.org/I3129830433"]}],"countries":["TZ"],"is_corresponding":false,"raw_author_name":"Said A.H. Vuai","raw_affiliation_strings":["Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mbeya University of Science and Technology, P. o. Box 131, Mbeya, Tanzania","institution_ids":["https://openalex.org/I3129830433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I3129830433"],"apc_list":{"value":1350,"currency":"USD","value_usd":1350},"apc_paid":{"value":1350,"currency":"USD","value_usd":1350},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.88713144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":null,"first_page":"100897","last_page":"100897"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12950","display_name":"Educational Environments and Student Outcomes","score":0.6044999957084656,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12950","display_name":"Educational Environments and Student Outcomes","score":0.6044999957084656,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.23319999873638153,"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/T12256","display_name":"Facilities and Workplace Management","score":0.03799999877810478,"subfield":{"id":"https://openalex.org/subfields/3207","display_name":"Social Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.6653000116348267},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5597000122070312},{"id":"https://openalex.org/keywords/combinatorial-optimization","display_name":"Combinatorial optimization","score":0.4763000011444092},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.43779999017715454},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.3682999908924103},{"id":"https://openalex.org/keywords/combinatorial-analysis","display_name":"Combinatorial analysis","score":0.3488999903202057}],"concepts":[{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.6653000116348267},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5597000122070312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5519999861717224},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.4763000011444092},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4002000093460083},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39149999618530273},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3682999908924103},{"id":"https://openalex.org/C2987825933","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorial analysis","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.32839998602867126},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.3077000081539154},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2946000099182129},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28139999508857727},{"id":"https://openalex.org/C38767284","wikidata":"https://www.wikidata.org/wiki/Q5601715","display_name":"Greedy coloring","level":5,"score":0.27889999747276306},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.26190000772476196}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.array.2026.100897","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.array.2026.100897","pdf_url":null,"source":{"id":"https://openalex.org/S4210194039","display_name":"Array","issn_l":"2590-0056","issn":["2590-0056"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Array","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/j.array.2026.100897","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.array.2026.100897","pdf_url":null,"source":{"id":"https://openalex.org/S4210194039","display_name":"Array","issn_l":"2590-0056","issn":["2590-0056"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Array","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.6595421433448792}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1983380249","https://openalex.org/W1994809982","https://openalex.org/W2011653811","https://openalex.org/W2024059393","https://openalex.org/W2124992259","https://openalex.org/W2127670720","https://openalex.org/W2170031843","https://openalex.org/W2577501736","https://openalex.org/W2604602069","https://openalex.org/W2610093420","https://openalex.org/W2750029605","https://openalex.org/W2790558725","https://openalex.org/W2916567729","https://openalex.org/W3038696366","https://openalex.org/W4389218970","https://openalex.org/W4396905142","https://openalex.org/W4402839479","https://openalex.org/W4408756461","https://openalex.org/W4410504928"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"an":[3],"optimization":[4],"approach":[5,72],"for":[6],"exam":[7],"seating":[8],"in":[9,21,50],"universities":[10],"with":[11,57,76],"limited":[12],"infrastructure,":[13],"based":[14],"on":[15],"a":[16,37,51,77,150],"mixed-course":[17],"allocation":[18,152],"model.":[19],"Students":[20],"different":[22],"courses":[23,49,132],"share":[24],"rooms":[25,75,92,105],"while":[26],"maintaining":[27],"spatial":[28],"separation":[29],"to":[30,123],"improve":[31],"academic":[32],"integrity.":[33],"The":[34,99,114,138],"model":[35,62,84,139],"incorporates":[36],"theoretical":[38],"probability":[39],"of":[40,47,80],"interaction,":[41],"which":[42],"decreases":[43],"as":[44],"the":[45,60,66,70,82,103],"number":[46],"mixed":[48],"room":[52],"increases.":[53],"Using":[54],"real":[55],"data":[56],"5175":[58],"students,":[59],"proposed":[61,83],"significantly":[63],"improves":[64],"upon":[65],"traditional":[67,71],"method.":[68],"Although":[69],"required":[73],"35":[74],"total":[78],"capacity":[79],"7269,":[81],"utilized":[85],"only":[86],"12":[87],"large":[88],"rooms,":[89],"leaving":[90],"23":[91],"unused":[93,100],"and":[94,130,136,145],"saving":[95],"about":[96],"2475":[97],"seats.":[98],"space":[101],"within":[102],"occupied":[104],"was":[106,117],"minimal":[107],"(approximately":[108],"29":[109],"seats),":[110],"indicating":[111],"near-optimal":[112],"utilization.":[113],"invigilation":[115],"requirement":[116],"reduced":[118],"from":[119],"at":[120],"least":[121],"70":[122],"36,":[124],"achieving":[125],"nearly":[126],"50%":[127],"savings.":[128],"Small-enrollment":[129],"carryover":[131],"are":[133],"efficiently":[134],"integrated":[135],"sorted.":[137],"is":[140],"formulated":[141],"using":[142],"graph":[143],"coloring":[144],"combinatorial":[146],"optimization,":[147],"supported":[148],"by":[149],"simple":[151],"algorithm.":[153]},"counts_by_year":[],"updated_date":"2026-05-28T06:12:49.907903","created_date":"2026-05-19T00:00:00"}