1.5-Approximation for treewidth of graphs excluding a graph with one crossing as a minor
We give polynomial-time constant-factor approximation algorithms for the treewidth and branchwidth of any H-minor-free graph for a given graph H with crossing number at most 1. The approximation factors are 1.5 for treewidth and 2.25 for branchwidth. In particular, our result directly applies to cla...
| 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:2117/97497 |
| Acceso en línea: | https://hdl.handle.net/2117/97497 |
| Access Level: | acceso abierto |
| Palabra clave: | Treewidth of graphs Polynomial-time constant-factor approximation algorithms Àrees temàtiques de la UPC::Informàtica |
| Sumario: | We give polynomial-time constant-factor approximation algorithms for the treewidth and branchwidth of any H-minor-free graph for a given graph H with crossing number at most 1. The approximation factors are 1.5 for treewidth and 2.25 for branchwidth. In particular, our result directly applies to classes of nonplanar graphs such as K_{5}-minor-free graphs and K_{3,3}-minor-free graphs. Along the way, we present a polynomial-time algorithm to decompose H-minor-free graphs into planar graphs and graphs of treewidth at most c_H (a constant dependent on H) using clique sums. This result has several applications in designing fully polynomial-time approximation schemes and fixed-parameter algorithms for many NP-complete problems on these graphs. |
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