  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 $O(\rm{poly}(k) \log n)$ bits (of working memory).
By using kernel cascades, we obtain the best known kernels in polynomial time
with $O(\rm{poly}(k) \log n)$ bits.
