{"id":"https://openalex.org/W4409444311","doi":"https://doi.org/10.1007/s10107-025-02220-5","title":"On the split closure of the periodic timetabling polytope","display_name":"On the split closure of the periodic timetabling polytope","publication_year":2025,"publication_date":"2025-04-15","ids":{"openalex":"https://openalex.org/W4409444311","doi":"https://doi.org/10.1007/s10107-025-02220-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-025-02220-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-025-02220-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-025-02220-5.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-025-02220-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042594597","display_name":"Niels Lindner","orcid":"https://orcid.org/0000-0002-8337-4387"},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Niels Lindner","raw_affiliation_strings":["Freie Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-8337-4387","affiliations":[{"raw_affiliation_string":"Freie Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042709277","display_name":"Berenike Masing","orcid":"https://orcid.org/0000-0001-7201-2412"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Berenike Masing","raw_affiliation_strings":["Zuse Institute Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0001-7201-2412","affiliations":[{"raw_affiliation_string":"Zuse Institute Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I195893171"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042594597"],"corresponding_institution_ids":["https://openalex.org/I75951250"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08728679,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"215","issue":"1-2","first_page":"325","last_page":"367"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T10551","display_name":"Scheduling and Optimization Algorithms","score":0.9983000159263611,"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/T11568","display_name":"Railway Systems and Energy Efficiency","score":0.9973999857902527,"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/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.9916999936103821,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7863693237304688},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.7851083278656006},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6797153949737549},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5224979519844055},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.444964200258255},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3322475552558899},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16853341460227966}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7863693237304688},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.7851083278656006},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6797153949737549},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5224979519844055},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.444964200258255},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3322475552558899},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16853341460227966},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10107-025-02220-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-025-02220-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-025-02220-5.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10107-025-02220-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-025-02220-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-025-02220-5.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1372115314","display_name":null,"funder_award_id":"EXC-2046","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2117824717","display_name":null,"funder_award_id":"project ID: 390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7354608348","display_name":null,"funder_award_id":"EXC-2046/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7362566262","display_name":null,"funder_award_id":"EXC-2046/1","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"},{"id":"https://openalex.org/G7725451807","display_name":"EXC 2046: MATH+: Berlin Mathematics Research Center","funder_award_id":"390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8964763783","display_name":null,"funder_award_id":"390685689","funder_id":"https://openalex.org/F4320330291","funder_display_name":"Berlin Mathematics Research Center MATH+"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320330291","display_name":"Berlin Mathematics Research Center MATH+","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409444311.pdf","grobid_xml":"https://content.openalex.org/works/W4409444311.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W28746272","https://openalex.org/W1596730848","https://openalex.org/W1970193303","https://openalex.org/W1975254220","https://openalex.org/W1976461547","https://openalex.org/W2010730730","https://openalex.org/W2014328192","https://openalex.org/W2021043398","https://openalex.org/W2034266713","https://openalex.org/W2081681998","https://openalex.org/W2083625505","https://openalex.org/W2105806740","https://openalex.org/W2113019421","https://openalex.org/W2123691634","https://openalex.org/W2125810408","https://openalex.org/W2148962278","https://openalex.org/W2168004511","https://openalex.org/W2579545464","https://openalex.org/W2748301739","https://openalex.org/W2804205549","https://openalex.org/W2921186940","https://openalex.org/W2950315005","https://openalex.org/W3090500580","https://openalex.org/W3093066651","https://openalex.org/W3176334095","https://openalex.org/W3185402193","https://openalex.org/W4213108070","https://openalex.org/W4244290607","https://openalex.org/W4300568640"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4280529077","https://openalex.org/W1493684871","https://openalex.org/W2886567582","https://openalex.org/W4390962314","https://openalex.org/W4289703404","https://openalex.org/W2999175164","https://openalex.org/W4387265813","https://openalex.org/W4286224459","https://openalex.org/W4320410061"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"Periodic":[2],"Event":[3],"Scheduling":[4],"Problem":[5],"(PESP)":[6],"is":[7,87,102,133],"the":[8,38,52,80,83,122,127,130,141,169,173,176],"central":[9],"mathematical":[10],"tool":[11],"for":[12,192],"periodic":[13],"timetable":[14],"optimization":[15],"in":[16,23,70,95],"public":[17],"transport.":[18],"PESP":[19,84],"can":[20,92,180],"be":[21,93,181],"formulated":[22],"several":[24],"ways":[25],"as":[26],"a":[27,61],"mixed-integer":[28,63],"linear":[29],"program":[30],"with":[31,51],"typically":[32],"general":[33,62],"integer":[34],"variables.":[35],"We":[36,98],"investigate":[37],"split":[39,47,58,142,160,185],"closure":[40],"of":[41,79,144,168,172,175],"these":[42],"formulations":[43],"and":[44,76,147,187],"show":[45,148],"that":[46,89,100,121,149],"inequalities":[48,59,67,91],"are":[49,60,68],"identical":[50],"recently":[53],"introduced":[54],"flip":[55,66,90,131],"inequalities.":[56],"While":[57],"programming":[64],"technique,":[65],"defined":[69],"purely":[71],"combinatorial":[72],"terms,":[73],"namely":[74],"cycles":[75],"arc":[77],"sets":[78],"digraph":[81],"underlying":[82],"instance.":[85],"It":[86],"known":[88],"separated":[94],"pseudo-polynomial":[96],"time.":[97],"prove":[99],"this":[101],"best":[103],"possible":[104],"unless":[105],"$$\\hbox":[106],"{P}=\\hbox":[107],"{NP}$$":[108],"<mml:math":[109],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[110],"<mml:mrow>":[111],"<mml:mtext>P</mml:mtext>":[112],"<mml:mo>=</mml:mo>":[113],"<mml:mtext>NP</mml:mtext>":[114],"</mml:mrow>":[115],"</mml:math>":[116],",":[117],"but":[118],"also":[119],"observe":[120],"complexity":[123],"becomes":[124],"linear-time":[125],"if":[126],"cycle":[128],"defining":[129],"inequality":[132],"fixed.":[134],"Moreover,":[135],"introducing":[136],"mixed-integer-compatible":[137],"maps,":[138],"we":[139,163],"compare":[140],"closures":[143],"different":[145],"formulations,":[146],"reformulation":[150],"or":[151],"binarization":[152],"by":[153,184],"subdivision":[154],"do":[155],"not":[156],"lead":[157],"to":[158],"stronger":[159],"closures.":[161],"Finally,":[162],"estimate":[164],"computationally":[165],"how":[166],"much":[167],"optimality":[170],"gap":[171],"instances":[174],"benchmark":[177],"library":[178],"PESPlib":[179],"closed":[182],"exclusively":[183],"cuts,":[186],"provide":[188],"better":[189],"dual":[190],"bounds":[191],"five":[193],"instances.":[194]},"counts_by_year":[],"updated_date":"2026-06-12T06:20:11.936012","created_date":"2025-10-10T00:00:00"}