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.

翻译：设$n$为参数化问题的规模，$k$为参数。我们提出了反馈顶点集、路径压缩与簇编辑/删除问题的核，其大小均为$k$的多项式，可在多项式时间及$O(\rm{poly}(k) \log n)$比特（工作内存）内计算。通过使用核级联方法，我们在多项式时间内以$O(\rm{poly}(k) \log n)$比特获得了目前已知的最优核。