Paper by Erik D. Demaine

Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dimitrios M. Thilikos, “Exponential Speedup of Fixed-Parameter Algorithms for Classes of Graphs Excluding Single-Crossing Graphs as Minors”, Algorithmica, volume 41, number 4, February 2005, pages 245–267.

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(49.55 √k nO(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.

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Related papers:
CliqueSum_ISAAC2002 (Exponential Speedup of Fixed-Parameter Algorithms on K3,3-minor-free or K5-minor-free Graphs)

See also other papers by Erik Demaine.
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Last updated March 12, 2024 by Erik Demaine.