Space-Efficient Graph Kernelizations

Abstract

Let $n$ be the size of a parameterized problem and $k$ the parameter. We present kernels for Feedback Vertex Set, Path Contraction and Cluster Editing/Deletion whose sizes are all polynomial in $k$ and that are computable in polynomial time and with $O(\mathrm{poly}(\mathrm{k})\log \mathrm{n})$ bits (of working memory). By using kernel cascades, we obtain the best known kernels in polynomial time with $O(\mathrm{poly}(\mathrm{k})\log \mathrm{n})$ bits.