{"id":"https://openalex.org/W2397446014","doi":"https://doi.org/10.1007/s10107-017-1134-7","title":"Maximum semidefinite and linear extension complexity of families of polytopes","display_name":"Maximum semidefinite and linear extension complexity of families of polytopes","publication_year":2017,"publication_date":"2017-03-24","ids":{"openalex":"https://openalex.org/W2397446014","doi":"https://doi.org/10.1007/s10107-017-1134-7","mag":"2397446014"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-017-1134-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-017-1134-7","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1605.08538","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020875207","display_name":"Gennadiy Averkov","orcid":"https://orcid.org/0000-0003-2245-9958"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Gennadiy Averkov","raw_affiliation_strings":["Institut f\u00fcr Mathematische Optimierung, Otto-von-Guericke-Universit\u00e4t Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","Otto von Guericke Universita\u0308t Magdeburg"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematische Optimierung, Otto-von-Guericke-Universit\u00e4t Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"Otto von Guericke Universita\u0308t Magdeburg","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062961656","display_name":"Volker Kaibel","orcid":"https://orcid.org/0000-0002-0388-7597"},"institutions":[{"id":"https://openalex.org/I95793202","display_name":"Otto-von-Guericke University Magdeburg","ror":"https://ror.org/00ggpsq73","country_code":"DE","type":"education","lineage":["https://openalex.org/I95793202"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Volker Kaibel","raw_affiliation_strings":["Institut f\u00fcr Mathematische Optimierung, Otto-von-Guericke-Universit\u00e4t Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","Otto von Guericke Universita\u0308t Magdeburg"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematische Optimierung, Otto-von-Guericke-Universit\u00e4t Magdeburg, Universit\u00e4tsplatz 2, 39106, Magdeburg, Germany","institution_ids":["https://openalex.org/I95793202"]},{"raw_affiliation_string":"Otto von Guericke Universita\u0308t Magdeburg","institution_ids":["https://openalex.org/I95793202"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023809656","display_name":"Stefan Weltge","orcid":"https://orcid.org/0000-0002-0102-8326"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Stefan Weltge","raw_affiliation_strings":["Institut f\u00fcr Operations Research, ETH Z\u00fcrich, R\u00e4mistrasse 101, 8092, Z\u00fcrich, Switzerland","ETH Z\u00fcrich"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Operations Research, ETH Z\u00fcrich, R\u00e4mistrasse 101, 8092, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"ETH Z\u00fcrich","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020875207"],"corresponding_institution_ids":["https://openalex.org/I95793202"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00437717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"167","issue":"2","first_page":"381","last_page":"394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9969000220298767,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9969000220298767,"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"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9945999979972839,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9557999968528748,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.802571713924408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7522147297859192},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7368167042732239},{"id":"https://openalex.org/keywords/linear-extension","display_name":"Linear extension","score":0.5706093907356262},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5540704131126404},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5424394011497498},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5166204571723938},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4981229305267334},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.4964187741279602},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4798114597797394},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47546786069869995},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4560967683792114},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4438205361366272},{"id":"https://openalex.org/keywords/integer-points-in-convex-polyhedra","display_name":"Integer points in convex polyhedra","score":0.4104486405849457},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3670611083507538},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.3615153133869171},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12082192301750183},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.0928792953491211},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09120321273803711}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.802571713924408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7522147297859192},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7368167042732239},{"id":"https://openalex.org/C129393996","wikidata":"https://www.wikidata.org/wiki/Q6553442","display_name":"Linear extension","level":3,"score":0.5706093907356262},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5540704131126404},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5424394011497498},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5166204571723938},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4981229305267334},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.4964187741279602},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4798114597797394},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47546786069869995},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4560967683792114},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4438205361366272},{"id":"https://openalex.org/C147700949","wikidata":"https://www.wikidata.org/wiki/Q6042594","display_name":"Integer points in convex polyhedra","level":4,"score":0.4104486405849457},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3670611083507538},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3615153133869171},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12082192301750183},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0928792953491211},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09120321273803711},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C123558587","wikidata":"https://www.wikidata.org/wiki/Q4956382","display_name":"Branch and price","level":3,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10107-017-1134-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-017-1134-7","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1605.08538","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.08538","pdf_url":"https://arxiv.org/pdf/1605.08538","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/130049","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/130049","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Programming, 167 (2)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.1605.08538","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1605.08538","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"},{"id":"doi:10.3929/ethz-b-000130049","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000130049","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"article-journal"},{"id":"mag:2397446014","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1605.08538","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1605.08538","pdf_url":"https://arxiv.org/pdf/1605.08538","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1564745785","https://openalex.org/W1858857015","https://openalex.org/W1942134738","https://openalex.org/W1945057103","https://openalex.org/W1967232806","https://openalex.org/W1974962384","https://openalex.org/W1990029940","https://openalex.org/W2025202934","https://openalex.org/W2031923588","https://openalex.org/W2033871299","https://openalex.org/W2061987651","https://openalex.org/W2068066892","https://openalex.org/W2068422506","https://openalex.org/W2095405086","https://openalex.org/W2119368733","https://openalex.org/W2138677859","https://openalex.org/W2139023954","https://openalex.org/W2159584454","https://openalex.org/W2337855014","https://openalex.org/W2593959808","https://openalex.org/W2963290197","https://openalex.org/W6638170056","https://openalex.org/W6655849190"],"related_works":["https://openalex.org/W2964171684","https://openalex.org/W2569588499","https://openalex.org/W2080072463","https://openalex.org/W2949953710","https://openalex.org/W2608930457","https://openalex.org/W3211971493","https://openalex.org/W2901191490","https://openalex.org/W2759253428","https://openalex.org/W2001834842","https://openalex.org/W3092492379","https://openalex.org/W2963756047","https://openalex.org/W2288091890","https://openalex.org/W1837134879","https://openalex.org/W3098872886","https://openalex.org/W1973868432","https://openalex.org/W2796815965","https://openalex.org/W1016068550","https://openalex.org/W1965650902","https://openalex.org/W1648365462","https://openalex.org/W852493970"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}