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...
| 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:2117/97525 |
| 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 |
| 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. |
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