# Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs

@inproceedings{vanBevern2011LinearTimeCO, title={Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs}, author={Ren{\'e} van Bevern and Sepp Hartung and Frank Kammer and Rolf Niedermeier and Mathias Weller}, booktitle={IPEC}, year={2011} }

We present a linear-time kernelization algorithm that transforms a given planar graph G with domination number γ(G) into a planar graph G′ of size O(γ(G)) with γ(G)=γ(G′). In addition, a minimum dominating set for G can be inferred from a minimum dominating set for G′. In terms of parameterized algorithmics, this implies a linear-size problem kernel for the NP-hard Dominating Set problem on planar graphs, where the kernelization takes linear time. This improves on previous kernelization…

## 18 Citations

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