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.

翻译：设 $n$ 为参数化问题的规模，$k$ 为参数。我们提出若干核，其大小均为 $k$ 的多项式，且可在多项式时间内以 $O(\rm{poly}(k) \log n)$ 比特（工作内存）计算。主要成果是反馈顶点集的一个此类核。此外，我们给出了路径收缩与聚类编辑/删除的完全核。通过级联核化技术，我们在多项式时间内以 $O(\rm{poly}(k) \log n)$ 比特获得了当前已知的最佳核。