Linear-Time Computation of a Linear Problem Kernel for Dominating Set on Planar Graphs [chapter]

René van Bevern, Sepp Hartung, Frank Kammer, Rolf Niedermeier, Mathias Weller
2012 Lecture Notes in Computer Science  
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
more » ... hms that provide linear-size kernels in cubic time.
doi:10.1007/978-3-642-28050-4_16 fatcat:cvbceyuhu5crnjtfyrt5v7mstm