{"id":"https://openalex.org/W2101636313","doi":"https://doi.org/10.22028/d291-25909","title":"Gomory-Chv\u00e1tal cutting planes and the elementary closure of Polyhedra","display_name":"Gomory-Chv\u00e1tal cutting planes and the elementary closure of Polyhedra","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2101636313","doi":"https://doi.org/10.22028/d291-25909","mag":"2101636313"},"language":"en","primary_location":{"id":"pmh:oai:publikationen.sulb.uni-saarland.de:20.500.11880/25965","is_oa":true,"landing_page_url":"http://doi.org/10.22028/D291-25909","pdf_url":"http://dx.doi.org/10.22028/D291-25909","source":{"id":"https://openalex.org/S4377196499","display_name":"Publications of the UdS (Saarland University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91712215","host_organization_name":"Saarland University","host_organization_lineage":["https://openalex.org/I91712215"],"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":"","raw_type":"doc-type:doctoralThesis"},"type":"dissertation","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://dx.doi.org/10.22028/D291-25909","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000598657","display_name":"Friedrich Eisenbrand","orcid":"https://orcid.org/0000-0001-7928-1076"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Eisenbrand, Friedrich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5000598657"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9994999766349792,"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":0.9994999766349792,"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":0.996999979019165,"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":0.9954000115394592,"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/mathematics","display_name":"Mathematics","score":0.8678992986679077},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7664172649383545},{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.7603811025619507},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7576453685760498},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.7416001558303833},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6969252824783325},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5752347707748413},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5461451411247253},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.44836634397506714},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.4301527440547943},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42945367097854614},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37415963411331177},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07789281010627747}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8678992986679077},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7664172649383545},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.7603811025619507},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7576453685760498},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.7416001558303833},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6969252824783325},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5752347707748413},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5461451411247253},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.44836634397506714},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.4301527440547943},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42945367097854614},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37415963411331177},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07789281010627747},{"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":8,"locations":[{"id":"pmh:oai:publikationen.sulb.uni-saarland.de:20.500.11880/25965","is_oa":true,"landing_page_url":"http://doi.org/10.22028/D291-25909","pdf_url":"http://dx.doi.org/10.22028/D291-25909","source":{"id":"https://openalex.org/S4377196499","display_name":"Publications of the UdS (Saarland University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91712215","host_organization_name":"Saarland University","host_organization_lineage":["https://openalex.org/I91712215"],"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":"","raw_type":"doc-type:doctoralThesis"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.337.2805","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.337.2805","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.math.uni-paderborn.de/fileadmin/Mathematik/AG-Eisenbrand/publications/diss.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:519777","is_oa":false,"landing_page_url":"http://edoc.mpg.de/519777","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"PhD-Thesis"},{"id":"pmh:oai:edoc.mpg.de:520626","is_oa":false,"landing_page_url":"http://edoc.mpg.de/520626","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"PhD-Thesis"},{"id":"pmh:oai:infoscience.epfl.ch:124915","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/124915","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pure.mpg.de:item_1330775","is_oa":false,"landing_page_url":"https://hdl.handle.net/11858/00-001M-0000-000F-3321-1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"info:eu-repo/semantics/doctoralThesis"},{"id":"doi:10.22028/d291-25909","is_oa":true,"landing_page_url":"https://doi.org/10.22028/d291-25909","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Collection"},{"id":"mag:2101636313","is_oa":false,"landing_page_url":"http://scidok.sulb.uni-saarland.de/volltexte/2007/1342/pdf/Dissertation_7143_Eise_Frie_2000.pdf","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:publikationen.sulb.uni-saarland.de:20.500.11880/25965","is_oa":true,"landing_page_url":"http://doi.org/10.22028/D291-25909","pdf_url":"http://dx.doi.org/10.22028/D291-25909","source":{"id":"https://openalex.org/S4377196499","display_name":"Publications of the UdS (Saarland University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91712215","host_organization_name":"Saarland University","host_organization_lineage":["https://openalex.org/I91712215"],"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":"","raw_type":"doc-type:doctoralThesis"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2101636313.pdf","grobid_xml":"https://content.openalex.org/works/W2101636313.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W307896644","https://openalex.org/W1490215229","https://openalex.org/W1523950960","https://openalex.org/W1557027117","https://openalex.org/W1568620904","https://openalex.org/W1592882366","https://openalex.org/W1604158939","https://openalex.org/W1655990431","https://openalex.org/W1867057885","https://openalex.org/W1940223960","https://openalex.org/W1963547452","https://openalex.org/W1968143987","https://openalex.org/W1970193303","https://openalex.org/W1979740015","https://openalex.org/W1985138225","https://openalex.org/W1990237439","https://openalex.org/W1995945562","https://openalex.org/W1996256832","https://openalex.org/W1997864729","https://openalex.org/W2002252750","https://openalex.org/W2008924211","https://openalex.org/W2009683816","https://openalex.org/W2011039300","https://openalex.org/W2011214860","https://openalex.org/W2011805810","https://openalex.org/W2017095313","https://openalex.org/W2021320246","https://openalex.org/W2029880758","https://openalex.org/W2032980094","https://openalex.org/W2033040247","https://openalex.org/W2038193643","https://openalex.org/W2044095368","https://openalex.org/W2049143039","https://openalex.org/W2051739235","https://openalex.org/W2062604685","https://openalex.org/W2069767473","https://openalex.org/W2083839413","https://openalex.org/W2093241008","https://openalex.org/W2100440346","https://openalex.org/W2102738679","https://openalex.org/W2104245397","https://openalex.org/W2106264302","https://openalex.org/W2113011069","https://openalex.org/W2114616381","https://openalex.org/W2123640521","https://openalex.org/W2127813745","https://openalex.org/W2145243417","https://openalex.org/W2158655916","https://openalex.org/W2161305900","https://openalex.org/W2166789519","https://openalex.org/W2169563629","https://openalex.org/W2326211873","https://openalex.org/W2327315803","https://openalex.org/W2334989808","https://openalex.org/W2340149117","https://openalex.org/W2492280620","https://openalex.org/W2752853835","https://openalex.org/W3175367423"],"related_works":["https://openalex.org/W1981135486","https://openalex.org/W1993333105"],"abstract_inverted_index":{"The":[0,29,43],"elementary":[1,38,110,129,160],"closure":[2,39,111,130,161],"P';":[3,19,143],"of":[4,11,36,50,68,79,112,140,154,162,200],"a":[5,21,113,120,163,175,186,197,203],"polyhedrom":[6],"P":[7,12,26],"is":[8,20,27,32,46,57,87,116,166],"the":[9,33,37,47,76,83,93,105,109,128,134,138,152,159],"intersection":[10],"with":[13,196],"all":[14],"its":[15],"Gomory-Chv\u00c3\u00a1tal":[16],"cutting":[17,183],"planes.":[18],"rational":[22,114,164],"polyhedron":[23,115,165],"provided":[24],"that":[25,75,104,151],"rational.":[28],"Chv\u00c3\u00a1tal-Gomory":[30],"procedure":[31],"iterative":[34],"application":[35],"operation":[40],"to":[41,53,157],"P.":[42],"Chv\u00c3\u00a1tal":[44,71,77],"rank":[45,78],"minimal":[48],"number":[49,139,153],"iterations":[51],"needed":[52,156],"obtain":[54],"P_I.":[55],"It":[56],"always":[58],"finite,":[59],"but":[60],"already":[61],"in":[62,82,131,169,178,193,202],"|R\u00c2\u00b2":[63],"one":[64],"can":[65],"construct":[66],"polytopes":[67,80],"arbitrary":[69],"large":[70],"rank.":[72],"We":[73,102,149],"show":[74,103,150],"contained":[81],"n-dimensional":[84],"0/1":[85],"cube":[86],"O(n\u00c2\u00b2":[88],"log":[89],"n)":[90],"and":[91],"prove":[92],"lower":[94],"bound":[95],"(1+E)":[96],"n,":[97],"for":[98,108,137,185],"some":[99],"E>":[100],"0.":[101],"separation":[106],"problem":[107,121],"NP-hard.":[117],"This":[118],"solves":[119],"posed":[122],"by":[123],"Schrijver.":[124],"Last":[125],"we":[126,173],"consider":[127],"fixed":[132,147,170,194],"dimension.":[133,148,171],"known":[135],"bounds":[136],"inequalities":[141,155],"defining":[142],"are":[144],"exponential,":[145],"even":[146],"describe":[158],"polynomially":[167],"bounded":[168],"Finally,":[172],"present":[174],"polynomial":[176,191],"algorithm":[177],"varying":[179],"dimension,":[180],"which":[181],"computes":[182],"planes":[184],"simplicial":[187],"cone":[188],"from":[189],"this":[190],"description":[192],"dimension":[195],"maximal":[198],"degree":[199],"violation":[201],"natural":[204],"sense.":[205]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}