Exponential Speedup of Fixed-Parameter Algorithms on K3, 3-Minor-Free or K5-Minor-Free Graphs

@inproceedings{Demaine2002ExponentialSO,
  title={Exponential Speedup of Fixed-Parameter Algorithms on K3, 3-Minor-Free or K5-Minor-Free Graphs},
  author={Erik D. Demaine and Mohammad Taghi Hajiaghayi and Dimitrios M. Thilikos},
  booktitle={ISAAC},
  year={2002}
}
We present a fixed parameter algorithm that constructively solves the k-dominating set problem on graphs excluding one of the K5 or K3,3 as a minor in time O(3 6 √ n). 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 K3,3(K5)-minor-free graphs as a special case. As a consequence, we extend our results to several other problems such as vertex cover, edge dominating… CONTINUE READING
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