The Hirsch conjecture has been disproved : an interview with Francisco Santos

The famous Hirsch conjecture was formulated in 1957 in a conversation of Warren Hirsch with George Dantzig, the father of the simplex method. It asserts that given a polytope of dimension d and n facets, its combinatorial diameter is smaller than or equal to n–d, i.e. any two vertices of the polytop...

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Autor: Miranda Galcerán, Eva|||0000-0001-9518-5279
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/17085
Acceso en línea:https://hdl.handle.net/2117/17085
https://dx.doi.org/10.4171/NEWS
Access Level:acceso abierto
Palabra clave:Simulation methods
Simulació, Mètodes de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
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spelling The Hirsch conjecture has been disproved : an interview with Francisco SantosMiranda Galcerán, Eva|||0000-0001-9518-5279Simulation methodsSimulació, Mètodes deÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::OptimitzacióThe famous Hirsch conjecture was formulated in 1957 in a conversation of Warren Hirsch with George Dantzig, the father of the simplex method. It asserts that given a polytope of dimension d and n facets, its combinatorial diameter is smaller than or equal to n–d, i.e. any two vertices of the polytope can be connected to each other by a path of at most n–d edges. The conjecture is related to the problem of complexity of the simplex method (it gives a lower bound). The conjecture has been open for 53 years and has attracted the interest of many mathematicians in discrete, combinatorial and computational geometry. The simplicity of its statement has also attracted mathematicians in other areas. On 10 May 2010, the entry about the Hirsch Conjecture in Wikipedia was updated, announcing that Francisco Santos had found a counterexample to the Hirsch conjecture. Later, on 14 June, Francisco Santos posted a preprint where the first counterexample was given. It was a polytope in dimension 43 and with 86 facets. The paper is now published in Annals of Mathematics [Sa4]. The HirschConjecture has been disproved.Peer Reviewed20122012-12-0120122012-12-10journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/17085https://dx.doi.org/10.4171/NEWSreponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/170852026-05-27T15:37:01Z
dc.title.none.fl_str_mv The Hirsch conjecture has been disproved : an interview with Francisco Santos
title The Hirsch conjecture has been disproved : an interview with Francisco Santos
spellingShingle The Hirsch conjecture has been disproved : an interview with Francisco Santos
Miranda Galcerán, Eva|||0000-0001-9518-5279
Simulation methods
Simulació, Mètodes de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
title_short The Hirsch conjecture has been disproved : an interview with Francisco Santos
title_full The Hirsch conjecture has been disproved : an interview with Francisco Santos
title_fullStr The Hirsch conjecture has been disproved : an interview with Francisco Santos
title_full_unstemmed The Hirsch conjecture has been disproved : an interview with Francisco Santos
title_sort The Hirsch conjecture has been disproved : an interview with Francisco Santos
dc.creator.none.fl_str_mv Miranda Galcerán, Eva|||0000-0001-9518-5279
author Miranda Galcerán, Eva|||0000-0001-9518-5279
author_facet Miranda Galcerán, Eva|||0000-0001-9518-5279
author_role author
dc.subject.none.fl_str_mv Simulation methods
Simulació, Mètodes de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
topic Simulation methods
Simulació, Mètodes de
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
description The famous Hirsch conjecture was formulated in 1957 in a conversation of Warren Hirsch with George Dantzig, the father of the simplex method. It asserts that given a polytope of dimension d and n facets, its combinatorial diameter is smaller than or equal to n–d, i.e. any two vertices of the polytope can be connected to each other by a path of at most n–d edges. The conjecture is related to the problem of complexity of the simplex method (it gives a lower bound). The conjecture has been open for 53 years and has attracted the interest of many mathematicians in discrete, combinatorial and computational geometry. The simplicity of its statement has also attracted mathematicians in other areas. On 10 May 2010, the entry about the Hirsch Conjecture in Wikipedia was updated, announcing that Francisco Santos had found a counterexample to the Hirsch conjecture. Later, on 14 June, Francisco Santos posted a preprint where the first counterexample was given. It was a polytope in dimension 43 and with 86 facets. The paper is now published in Annals of Mathematics [Sa4]. The HirschConjecture has been disproved.
publishDate 2012
dc.date.none.fl_str_mv 2012
2012-12-01
2012
2012-12-10
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/17085
https://dx.doi.org/10.4171/NEWS
url https://hdl.handle.net/2117/17085
https://dx.doi.org/10.4171/NEWS
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
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Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
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