{"id":"https://openalex.org/W2497426325","doi":"https://doi.org/10.1007/s10479-016-2220-6","title":"Modeling high school timetabling with bitvectors","display_name":"Modeling high school timetabling with bitvectors","publication_year":2016,"publication_date":"2016-07-22","ids":{"openalex":"https://openalex.org/W2497426325","doi":"https://doi.org/10.1007/s10479-016-2220-6","mag":"2497426325","pmid":"https://pubmed.ncbi.nlm.nih.gov/28529399"},"language":"en","primary_location":{"id":"doi:10.1007/s10479-016-2220-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-016-2220-6","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10479-016-2220-6.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10479-016-2220-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019385762","display_name":"Emir Demirovi\u0107","orcid":"https://orcid.org/0000-0003-1587-5582"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Emir Demirovi\u0107","raw_affiliation_strings":["Database and Artificial Intelligence Group, Technische Universit\u00e4t Wien, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Database and Artificial Intelligence Group, Technische Universit\u00e4t Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084546772","display_name":"Nysret Musliu","orcid":"https://orcid.org/0000-0002-3992-8637"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Nysret Musliu","raw_affiliation_strings":["Database and Artificial Intelligence Group, Technische Universit\u00e4t Wien, Vienna, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Database and Artificial Intelligence Group, Technische Universit\u00e4t Wien, Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019385762"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":0.6811,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76958014,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"252","issue":"2","first_page":"215","last_page":"238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9998000264167786,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11902","display_name":"Intelligent Tutoring Systems and Adaptive Learning","score":0.9458000063896179,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/computer-science","display_name":"Computer science","score":0.779279351234436},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.7040557861328125},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6877371072769165},{"id":"https://openalex.org/keywords/simulated-annealing","display_name":"Simulated annealing","score":0.6765470504760742},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6079159379005432},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5830549597740173},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.539753258228302},{"id":"https://openalex.org/keywords/hill-climbing","display_name":"Hill climbing","score":0.5028924345970154},{"id":"https://openalex.org/keywords/constraint-programming","display_name":"Constraint programming","score":0.49377235770225525},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.4882109463214874},{"id":"https://openalex.org/keywords/local-search","display_name":"Local search (optimization)","score":0.47788727283477783},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.4580923020839691},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.44375625252723694},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32468003034591675},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27262571454048157},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1274724006652832},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.07757449150085449}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.779279351234436},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7040557861328125},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6877371072769165},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.6765470504760742},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6079159379005432},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5830549597740173},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.539753258228302},{"id":"https://openalex.org/C135450995","wikidata":"https://www.wikidata.org/wiki/Q820272","display_name":"Hill climbing","level":2,"score":0.5028924345970154},{"id":"https://openalex.org/C173404611","wikidata":"https://www.wikidata.org/wiki/Q528588","display_name":"Constraint programming","level":3,"score":0.49377235770225525},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.4882109463214874},{"id":"https://openalex.org/C135320971","wikidata":"https://www.wikidata.org/wiki/Q1868524","display_name":"Local search (optimization)","level":2,"score":0.47788727283477783},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.4580923020839691},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44375625252723694},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32468003034591675},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27262571454048157},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1274724006652832},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.07757449150085449},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10479-016-2220-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-016-2220-6","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10479-016-2220-6.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},{"id":"pmid:28529399","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28529399","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of operations research","raw_type":"Journal Article"},{"id":"pmh:oai:europepmc.org:4284944","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5411413","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:RePEc:spr:annopr:v:252:y:2017:i:2:d:10.1007_s10479-016-2220-6","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10479-016-2220-6","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:repositum.tuwien.ac.at:1746085","is_oa":true,"landing_page_url":"http://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-2878","pdf_url":null,"source":{"id":"https://openalex.org/S4306400493","display_name":"reposiTUm (TU Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145847075","host_organization_name":"TU Wien","host_organization_lineage":["https://openalex.org/I145847075"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:repositum.tuwien.at:20.500.12708/338","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12708/338","pdf_url":null,"source":{"id":"https://openalex.org/S4306400493","display_name":"reposiTUm (TU Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145847075","host_organization_name":"TU Wien","host_organization_lineage":["https://openalex.org/I145847075"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10479-016-2220-6","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10479-016-2220-6","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10479-016-2220-6.pdf","source":{"id":"https://openalex.org/S57667410","display_name":"Annals of Operations Research","issn_l":"0254-5330","issn":["0254-5330","1572-9338"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4699999988079071,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[{"id":"https://openalex.org/G1528991492","display_name":"Artifical Intelligence in Employee Scheduling","funder_award_id":"P 24814","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321691","display_name":"Universit\u00e4t Wien","ror":"https://ror.org/03prydq77"},{"id":"https://openalex.org/F4320322839","display_name":"Technische Universit\u00e4t Wien","ror":"https://ror.org/04d836q62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2497426325.pdf","grobid_xml":"https://content.openalex.org/works/W2497426325.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1480909796","https://openalex.org/W1985195201","https://openalex.org/W2002696721","https://openalex.org/W2004417381","https://openalex.org/W2006146932","https://openalex.org/W2014684461","https://openalex.org/W2017615131","https://openalex.org/W2041129931","https://openalex.org/W2149331957","https://openalex.org/W2159920763","https://openalex.org/W2164237033","https://openalex.org/W2189049166","https://openalex.org/W2197786949","https://openalex.org/W2245155999","https://openalex.org/W2295061292","https://openalex.org/W2601606742","https://openalex.org/W2615276600","https://openalex.org/W2741684966","https://openalex.org/W3045900701","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4237368524","https://openalex.org/W3046481193","https://openalex.org/W90886653","https://openalex.org/W2041592502","https://openalex.org/W1551554231","https://openalex.org/W2114712485","https://openalex.org/W2123829500","https://openalex.org/W3043746022","https://openalex.org/W1245780190","https://openalex.org/W57712993"],"abstract_inverted_index":{"High":[0],"school":[1],"timetabling":[2],"(HSTT)":[3],"is":[4,33,146],"a":[5,40,56],"well":[6],"known":[7],"and":[8,22,37,119,136],"wide":[9],"spread":[10],"problem.":[11,150],"The":[12,139],"problem":[13],"consists":[14],"of":[15,46,68,83],"coordinating":[16],"resources":[17],"(e.g.":[18,24],"teachers,":[19],"rooms),":[20],"times,":[21],"events":[23],"lectures)":[25],"with":[26,101],"respect":[27],"to":[28,35,51,98,122],"various":[29],"constraints.":[30],"Unfortunately,":[31],"HSTT":[32,47,61,71,91,100],"hard":[34],"solve":[36,99],"just":[38],"finding":[39],"feasible":[41],"solution":[42],"for":[43,60,114,148],"simple":[44],"variants":[45],"has":[48],"been":[49],"proven":[50],"be":[52,73,96],"NP-complete.":[53],"We":[54,110],"propose":[55],"new":[57],"modeling":[58,117],"approach":[59,118,145],"using":[62,75,154],"bitvectors":[63],"in":[64],"which":[65],"constraint":[66,84],"costs":[67,85],"the":[69,112,123,161],"general":[70],"can":[72,95],"calculated":[74],"bit":[76],"operations.":[77],"This":[78],"model":[79],"allows":[80],"efficient":[81],"computation":[82],"making":[86],"it":[87,94,121],"useful":[88,147],"when":[89,127],"implementing":[90],"algorithms.":[92],"Additionally,":[93],"used":[97],"satisfiability":[102],"modulo":[103],"theory":[104],"(SMT)":[105],"solvers":[106],"that":[107,143],"support":[108],"bitvectors.":[109],"evaluate":[111],"performance":[113],"our":[115,144],"bitvector":[116],"compare":[120],"leading":[124],"engine":[125],"KHE":[126],"developing":[128],"local":[129],"search":[130],"algorithms":[131],"such":[132],"as":[133],"hill":[134],"climbing":[135],"simulated":[137],"annealing.":[138],"experimental":[140,152],"results":[141,153],"show":[142],"this":[149],"Furthermore,":[151],"SMT":[155],"are":[156],"given":[157],"on":[158],"instances":[159],"from":[160],"ITC":[162],"2011":[163],"benchmark":[164],"repository.":[165]},"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}