{"id":"https://openalex.org/W1598023462","doi":"https://doi.org/10.1007/978-3-642-40450-4_61","title":"The Recognition of Simple-Triangle Graphs and of Linear-Interval Orders Is Polynomial","display_name":"The Recognition of Simple-Triangle Graphs and of Linear-Interval Orders Is Polynomial","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1598023462","doi":"https://doi.org/10.1007/978-3-642-40450-4_61","mag":"1598023462"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-40450-4_61","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-40450-4_61","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1210.4352","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018078197","display_name":"George B. Mertzios","orcid":"https://orcid.org/0000-0001-7182-585X"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"George B. Mertzios","raw_affiliation_strings":["School of Engineering and Computing Sciences, Durham University, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Computing Sciences, Durham University, UK","institution_ids":["https://openalex.org/I190082696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018078197"],"corresponding_institution_ids":["https://openalex.org/I190082696"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.5449,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55141658,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":"3","first_page":"1150","last_page":"1185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9997000098228455,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/combinatorics","display_name":"Combinatorics","score":0.8513005375862122},{"id":"https://openalex.org/keywords/trapezoid-graph","display_name":"Trapezoid graph","score":0.8062053918838501},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.7243989109992981},{"id":"https://openalex.org/keywords/interval-graph","display_name":"Interval graph","score":0.7046625018119812},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.70415198802948},{"id":"https://openalex.org/keywords/permutation-graph","display_name":"Permutation graph","score":0.6756111979484558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6719456315040588},{"id":"https://openalex.org/keywords/maximal-independent-set","display_name":"Maximal independent set","score":0.5929221510887146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5836344361305237},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.5494248270988464},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4522344768047333},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.45188578963279724},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4482630491256714},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.44095325469970703},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4229482114315033},{"id":"https://openalex.org/keywords/intersection-graph","display_name":"Intersection graph","score":0.4213272035121918},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.41182011365890503},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.38670939207077026},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.30907177925109863},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2603163719177246}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8513005375862122},{"id":"https://openalex.org/C10325715","wikidata":"https://www.wikidata.org/wiki/Q7835582","display_name":"Trapezoid graph","level":5,"score":0.8062053918838501},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.7243989109992981},{"id":"https://openalex.org/C67810366","wikidata":"https://www.wikidata.org/wiki/Q835942","display_name":"Interval graph","level":5,"score":0.7046625018119812},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.70415198802948},{"id":"https://openalex.org/C68965932","wikidata":"https://www.wikidata.org/wiki/Q7169369","display_name":"Permutation graph","level":3,"score":0.6756111979484558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6719456315040588},{"id":"https://openalex.org/C18359143","wikidata":"https://www.wikidata.org/wiki/Q7888149","display_name":"Maximal independent set","level":5,"score":0.5929221510887146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5836344361305237},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.5494248270988464},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4522344768047333},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.45188578963279724},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4482630491256714},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44095325469970703},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4229482114315033},{"id":"https://openalex.org/C54540088","wikidata":"https://www.wikidata.org/wiki/Q3498041","display_name":"Intersection graph","level":4,"score":0.4213272035121918},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.41182011365890503},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.38670939207077026},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30907177925109863},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2603163719177246},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.1007/978-3-642-40450-4_61","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-40450-4_61","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"doi:10.1137/140963108","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140963108","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dro.dur.ac.uk.OAI2:13472","is_oa":false,"landing_page_url":"http://dro.dur.ac.uk/13472/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Bodlaender, Hans L. &amp; Italiano, Giuseppe F. (Eds.). (2013). Algorithms - ESA 2013 : 21st annual European symposium, Sophia Antipolis, France, September 2-4, 2013. Proceedings. Berlin, Heidelberg: Springer, pp. 719-730, Lecture notes in computer science(8125)","raw_type":"Book chapter"},{"id":"pmh:oai:dro.dur.ac.uk.OAI2:15767","is_oa":false,"landing_page_url":"http://dro.dur.ac.uk/15767/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"SIAM journal on discrete mathematics, 2015, Vol.29(3), pp.1150-1185 [Peer Reviewed Journal]","raw_type":"Article"},{"id":"pmh:oai:arXiv.org:1210.4352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1210.4352","pdf_url":"https://arxiv.org/pdf/1210.4352","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"mag:1598023462","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1210.4352.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.3122","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.3122","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.dur.ac.uk/george.mertzios/papers/Conf/Conf_PI-graphs_Linear-Interval-orders.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.699.6051","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.699.6051","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://community.dur.ac.uk/george.mertzios/papers/Conf/Conf_PI-graphs_Linear-Interval-orders.pdf","raw_type":"text"},{"id":"pmh:oai:durham-repository.worktribe.com:1406023","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1406023","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"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":"Journal Article"},{"id":"doi:10.48550/arxiv.1210.4352","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1210.4352","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1210.4352","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1210.4352","pdf_url":"https://arxiv.org/pdf/1210.4352","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1111885211","display_name":null,"funder_award_id":"EP/G043434/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6214505137","display_name":null,"funder_award_id":"EP/K022660/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7325551107","display_name":"Algorithmic Aspects of Intersection Graph Models","funder_award_id":"EP/K022660/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W639947448","https://openalex.org/W1579049696","https://openalex.org/W1597014679","https://openalex.org/W1854915859","https://openalex.org/W1954157972","https://openalex.org/W1972965975","https://openalex.org/W1983547967","https://openalex.org/W2003160050","https://openalex.org/W2010733068","https://openalex.org/W2019589107","https://openalex.org/W2026581241","https://openalex.org/W2047899424","https://openalex.org/W2049670817","https://openalex.org/W2055650273","https://openalex.org/W2086965047","https://openalex.org/W2143474538","https://openalex.org/W2151719453","https://openalex.org/W2170157130","https://openalex.org/W2584881854","https://openalex.org/W3135965400","https://openalex.org/W4237681658"],"related_works":["https://openalex.org/W2963089667","https://openalex.org/W2552250629","https://openalex.org/W2407258439","https://openalex.org/W2694242219","https://openalex.org/W1805397736","https://openalex.org/W2949641092","https://openalex.org/W2530575142","https://openalex.org/W3168576739","https://openalex.org/W2031276298","https://openalex.org/W3135451832","https://openalex.org/W2047570770","https://openalex.org/W3099519164","https://openalex.org/W3192294531","https://openalex.org/W1570340896","https://openalex.org/W2169829403","https://openalex.org/W3091696729","https://openalex.org/W2963418598","https://openalex.org/W299114843","https://openalex.org/W2112212574","https://openalex.org/W2029854525"],"abstract_inverted_index":{"Intersection":[0],"graphs":[1,23,47,53,60,95,124,134,161],"of":[2,61,96,106,132,182,188,192,219,232,251,269],"geometric":[3],"objects":[4],"have":[5,258],"been":[6,259,274],"extensively":[7,260],"studied,":[8],"both":[9,38],"due":[10],"to":[11,128],"their":[12,16,141],"interesting":[13],"structure":[14],"and":[15,24,40,74,88,102,105,111,122,145,209,239,262],"numerous":[17],"applications;":[18],"prominent":[19],"examples":[20],"include":[21],"interval":[22,39,76,214],"permutation":[25,41,87,121],"graphs.":[26,45],"In":[27,150,242],"this":[28,151,155],"paper":[29,152],"we":[30,153],"study":[31],"a":[32,67,70,78,169,175,206],"natural":[33],"graph":[34],"class":[35,256],"that":[36,63,159,228],"generalizes":[37],"graphs,":[42,90],"namely":[43,185],"simple-triangle":[44,133,160],"Simple-triangle":[46],"\u2013":[48,56],"also":[49,173],"known":[50,127],"as":[51],"PI":[52],"(for":[54],"Point-Interval)":[55],"are":[57,64,92,125,229,248],"the":[58,93,130,180,186,220,230,249,254,266],"intersection":[59,94,231,250],"triangles":[62],"defined":[65],"by":[66,143,157],"point":[68],"on":[69,77,223],"line":[71,80,97],"L":[72,81,100,103,109,112],"1":[73,101,110,198,204],"an":[75,137,213],"parallel":[79],"2.":[82],"They":[83],"lie":[84],"naturally":[85],"between":[86,99,108],"trapezoid":[89,123],"which":[91,247],"segments":[98],"2":[104,211],"trapezoids":[107],"2,":[113,201],"respectively.":[114],"Although":[115],"various":[116],"efficient":[117],"recognition":[118,131,187,271],"algorithms":[119],"for":[120],"well":[126],"exist,":[129],"has":[135,273],"remained":[136],"open":[138,177],"problem":[139,156,178],"since":[140],"introduction":[142],"Corneil":[144],"Kamula":[146],"three":[147],"decades":[148],"ago.":[149],"resolve":[154],"proving":[158],"can":[162],"be":[163],"recognized":[164],"in":[165,179,263],"polynomial":[166],"time.":[167],"As":[168],"consequence,":[170],"our":[171],"algorithm":[172],"solves":[174],"longstanding":[176],"area":[181],"partial":[183,193,225,244],"orders,":[184,190],"linear-interval":[189],"i.e.":[191],"orders":[194,226,233,245,252],"P":[195,197,200,203,210,227,246],"=":[196],"\u2229":[199],"where":[202],"is":[205,212,217],"linear":[207],"order":[208],"order.":[215],"This":[216],"one":[218],"first":[221],"results":[222],"recognizing":[224],"from":[234,253],"two":[235],"different":[236],"classes":[237],"$\\mathcal{P}_{1}$":[238],"$\\mathcal{P}_{2}$":[240],".":[241],"contrast,":[243],"same":[255],"$\\mathcal{P}$":[257],"investigated,":[261],"most":[264],"cases":[265],"complexity":[267],"status":[268],"these":[270],"problems":[272],"established.":[275]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
