New upper bounds on the decomposability of planar graphs and fixed parameter algorithms
It is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-w...
| Autores: | , |
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 2002 |
| 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:2117/97430 |
| Acceso en línea: | https://hdl.handle.net/2117/97430 |
| Access Level: | acceso abierto |
| Palabra clave: | Planar graphs Decomposability Fixed parameter algorithms Tree-width Branch-width Separation theorems Vertex cover Dominating set Àrees temàtiques de la UPC::Informàtica |
| Sumario: | It is known that a planar graph on n vertices has branch-width/tree-width bounded by alphasqrt{n}. In many algorithmic applications it is useful to have a small bound on the constant alpha. We give a proof of the best, so far, upper bound for the constant alpha. In particular, for the case of tree-width, alpha<3.182 and for the case of branch-width, alpha<2.122. Our proof is based on the planar separation theorem of Alon, Seymour & Thomas and some min-max theorem of the graph minors series. Based on these bounds we introduce a new method for solving different fixed parameter problems on planar graphs. We prove that our method provides the best so far exponential speed-up for fundamental problems on planar graphs like Vertex Cover, Dominating Set, Independent Set and many others. |
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