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...

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Detalles Bibliográficos
Autores: Demaine, Erik D., Hajiaghayi, Mohammad Taghi, Thilikos Touloupas, Dimitrios
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
Descripción
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.