Exponential speedup of fixed parameter algorithms on K_{3,3}-minor-free or K_{5}-minor-free graphs

We present a fixed parameter algorithm that constructively solves the k-dominating set problem on graphs excluding one of the K_{5} or K_3,3 as a minor in time O(3^{6sqrt{34 k}}n^{O(1)}). In fact, we present our algorithm for any H-minor-free graph where H is a single-crossing graph (can be drawn on...

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Detalles Bibliográficos
Autores: Hajiaghayi, Mohammad Taghi, Demaine, Erik D., 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:2117/97525
Acceso en línea:https://hdl.handle.net/2117/97525
Access Level:acceso abierto
Palabra clave:Fixed parameter algorithm
Exponential speedup
Àrees temàtiques de la UPC::Informàtica::Programació
Descripción
Sumario:We present a fixed parameter algorithm that constructively solves the k-dominating set problem on graphs excluding one of the K_{5} or K_3,3 as a minor in time O(3^{6sqrt{34 k}}n^{O(1)}). In fact, we present our algorithm for any H-minor-free graph where H is a single-crossing graph (can be drawn on the plane with at most one crossing) and obtain the algorithm for K_{3,3} (K_{5})-minor-free graphs as a special case. As a consequence, we extend our results to several other problems such as vertex cover, edge dominating set, independent set, clique-transversal set, kernels in digraphs, feedback vertex set and a series of vertex removal problems. Our work generalizes and extends the recent result of exponential speedup in designing fixed-parameter algorithms on planar graphs due to Alber et al. to other (non-planar) classes of graphs.