## Exponential Speedup of Fixed-Parameter Algorithms for Classes of Graphs Excluding Single-Crossing Graphs as Minors (2002)

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Citations: | 5 - 4 self |

### BibTeX

@MISC{Demaine02exponentialspeedup,

author = {Erik D. Demaine and MohammadTaghi Hajiaghayi and Dimitrios M. Thilikos},

title = {Exponential Speedup of Fixed-Parameter Algorithms for Classes of Graphs Excluding Single-Crossing Graphs as Minors },

year = {2002}

}

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### Abstract

We present a fixed-parameter algorithm that constructively solves the k-dominating set problem on any class of graphs excluding a single-crossing graph (a graph that can be drawn in the plane with at most one crossing) as a minor in O(4 9.55 √ k n O(1) ) time. Examples of such graph classes are the K3,3-minor-free graphs and the K5-minor-free graphs. 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 collection of vertex-removal problems. Our work generalizes and extends the recent results of exponential speedup in designing fixed-parameter algorithms on planar graphs due to Alber et al. to other (nonplanar) classes of graphs.