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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| 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 |
| Sumario: | 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. |
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