Space-Efficient Graph Kernelizations

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