Diameter of simplicial complexes, a computational approach.
ABSTRACT: The computational complexity of the simplex method, widely used for linear programming, depends on the combinatorial diameter of the edge graph of a polyhedron with n facets and dimension d. Despite its popularity, little is known about the (combinatorial) diameter of polytopes, and even f...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/9379 |
| Acceso en línea: | http://hdl.handle.net/10902/9379 |
| Access Level: | acceso abierto |
| Palabra clave: | Discrete Geometry Computational Geometry Simulated Annealing Simplicial Complex Combinatorial Diameter Geometría discreta Geometría computacional Enfriamiento simulado Complejo simplicial Diámetro combinatorio |
| Sumario: | ABSTRACT: The computational complexity of the simplex method, widely used for linear programming, depends on the combinatorial diameter of the edge graph of a polyhedron with n facets and dimension d. Despite its popularity, little is known about the (combinatorial) diameter of polytopes, and even for simpler types of complexes. For the case of polytopes, it was conjectured by Hirsch (1957) that the diameter is smaller than (n - d), but this was disproved by Francisco Santos (2010). In this thesis, we present two main results. First, a lower bound on the maximum diameter for two classes of simplicial complexes: pure simplicial complexes and pseudo-manifolds. Second, a topological improvement of Santos’ counter example to the Hirsch Conjecture. This one is (slightly) smaller than the previously known smallest simplicial non-Hirsch sphere. |
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