{"id":"https://openalex.org/W2069003940","doi":"https://doi.org/10.1007/s11083-012-9264-2","title":"On-Line Dimension of Semi-Orders","display_name":"On-Line Dimension of Semi-Orders","publication_year":2012,"publication_date":"2012-06-14","ids":{"openalex":"https://openalex.org/W2069003940","doi":"https://doi.org/10.1007/s11083-012-9264-2","mag":"2069003940"},"language":"en","primary_location":{"id":"doi:10.1007/s11083-012-9264-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-012-9264-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-012-9264-2.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"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":"Order","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/s11083-012-9264-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038469350","display_name":"Bart\u0142omiej Bosek","orcid":"https://orcid.org/0000-0001-8756-3663"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Bart\u0142omiej Bosek","raw_affiliation_strings":["Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","[Jagiellonian University]"],"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"[Jagiellonian University]","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004673481","display_name":"Kamil Kloch","orcid":null},"institutions":[{"id":"https://openalex.org/I186354981","display_name":"University of Passau","ror":"https://ror.org/05ydjnb78","country_code":"DE","type":"education","lineage":["https://openalex.org/I186354981"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kamil Kloch","raw_affiliation_strings":["Embedded Systems Lab, University of Passau, Passau, Germany","University Of Passau#TAB#"],"affiliations":[{"raw_affiliation_string":"Embedded Systems Lab, University of Passau, Passau, Germany","institution_ids":["https://openalex.org/I186354981"]},{"raw_affiliation_string":"University Of Passau#TAB#","institution_ids":["https://openalex.org/I186354981"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010286238","display_name":"Tomasz Krawczyk","orcid":"https://orcid.org/0000-0002-3093-2584"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Tomasz Krawczyk","raw_affiliation_strings":["Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","[Jagiellonian University]"],"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"[Jagiellonian University]","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107964690","display_name":"Piotr Micek","orcid":"https://orcid.org/0000-0001-9796-5375"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Micek","raw_affiliation_strings":["Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","[Jagiellonian University]"],"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"[Jagiellonian University]","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5038469350"],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.4459,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.73165417,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"30","issue":"2","first_page":"593","last_page":"615"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9848999977111816,"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"}},"topics":[{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9848999977111816,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9722999930381775,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9352999925613403,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7855699062347412},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7225547432899475},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.719707727432251},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7147709727287292},{"id":"https://openalex.org/keywords/order-type","display_name":"Order type","score":0.6835157871246338},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5780813694000244},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5671002864837646},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.5287313461303711},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.4853750467300415},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4777728319168091},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.43648576736450195},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43618083000183105},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41843998432159424},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4156702160835266},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10318529605865479},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10019418597221375},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0917515754699707}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7855699062347412},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7225547432899475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.719707727432251},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7147709727287292},{"id":"https://openalex.org/C138890893","wikidata":"https://www.wikidata.org/wiki/Q620006","display_name":"Order type","level":2,"score":0.6835157871246338},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5780813694000244},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5671002864837646},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.5287313461303711},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4853750467300415},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4777728319168091},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.43648576736450195},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43618083000183105},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41843998432159424},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4156702160835266},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10318529605865479},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10019418597221375},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0917515754699707},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11083-012-9264-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-012-9264-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-012-9264-2.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"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":"Order","raw_type":"journal-article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/181","is_oa":true,"landing_page_url":"http://ruj.uj.edu.pl/xmlui/handle/item/181","pdf_url":null,"source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s11083-012-9264-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11083-012-9264-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11083-012-9264-2.pdf","source":{"id":"https://openalex.org/S121371512","display_name":"Order","issn_l":"0167-8094","issn":["0167-8094","1572-9273"],"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":"Order","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069003940.pdf","grobid_xml":"https://content.openalex.org/works/W2069003940.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W170065150","https://openalex.org/W627977332","https://openalex.org/W1978730176","https://openalex.org/W1984477615","https://openalex.org/W1996768648","https://openalex.org/W1998185290","https://openalex.org/W2019109095","https://openalex.org/W2029134832","https://openalex.org/W2051677046","https://openalex.org/W2071546053","https://openalex.org/W2090372555","https://openalex.org/W2101652693","https://openalex.org/W2147737694","https://openalex.org/W2151140709","https://openalex.org/W2166858292","https://openalex.org/W4213282325"],"related_works":["https://openalex.org/W1972035260","https://openalex.org/W2794488505","https://openalex.org/W4301594054","https://openalex.org/W3086618278","https://openalex.org/W3125889879","https://openalex.org/W3124422538","https://openalex.org/W2295467472","https://openalex.org/W2470727813","https://openalex.org/W2017222821","https://openalex.org/W2835275266"],"abstract_inverted_index":{"We":[0,111],"analyze":[1,112],"the":[2,46,55,62,65,70,77,81,113,142],"on-line":[3,29,114],"dimension":[4,115],"of":[5,12,31,48,64,76,95,116,128,139,153],"partially":[6],"ordered":[7],"sets":[8],"as":[9],"a":[10,13,39,88,122,133],"value":[11,75],"two-person":[14],"game":[15,21,78],"between":[16],"Algorithm":[17,41,58,86],"and":[18,136],"Spoiler.":[19],"The":[20,74],"is":[22,80],"played":[23],"in":[24,69],"rounds.":[25],"Spoiler":[26,91],"presents":[27],"an":[28,150],"order":[30,94],"width":[32,96,129],"at":[33,38,97],"most":[34,98],"w,":[35],"one":[36],"point":[37],"time.":[40],"maintains":[42],"its":[43],"realizer,":[44],"i.e.,":[45,118],"set":[47],"d":[49,83],"linear":[50,72],"extensions":[51],"which":[52],"intersect":[53],"to":[54],"presented":[56],"order.":[57],"may":[59],"not":[60],"change":[61],"ordering":[63],"previously":[66],"introduced":[67],"elements":[68],"existing":[71],"extensions.":[73],"val(w)":[79],"least":[82],"such":[84],"that":[85,105],"has":[87],"strategy":[89],"against":[90],"presenting":[92],"any":[93],"w.":[99,140],"For":[100,125],"interval":[101,119],"orders":[102,120],"Hopkins":[103],"showed":[104],"val":[106],"$(w)":[107],"\\leqslant":[108],"4w-4$":[109],".":[110],"semi-orders":[117,127],"admitting":[121],"unit-length":[123],"representation.":[124],"up-growing":[126],"w":[130],"we":[131,148],"prove":[132],"matching":[134],"lower":[135],"upper":[137,151],"bound":[138,152],"In":[141],"general":[143],"(not":[144],"necessarily":[145],"up-growing)":[146],"case":[147],"provide":[149],"2w.":[154]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}
