In this paper, we devise a scheme for kernelizing, in sublinear space and polynomial time, various problems on planar graphs. The scheme exploits planarity to ensure that the resulting algorithms run in polynomial time and use O((sqrt(n) + k) log n) bits of space, where n is the number of vertices in the input instance and k is the intended solution size. As examples, we apply the scheme to Dominating Set and Vertex Cover. For Dominating Set, we also show that a well-known kernelization algorithm due to Alber et al. (JACM 2004) can be carried out in polynomial time and space O(k log n). Along the way, we devise restricted-memory procedures for computing region decompositions and approximating the aforementioned problems, which might be of independent interest.

翻译：本文提出了一种在亚线性空间和多项式时间内对平面图上多种问题进行核化的方案。该方案利用平面性确保所得算法在多项式时间内运行，且使用O((√n + k) log n)比特空间（其中n为输入实例的顶点数，k为预期解规模）。以支配集和顶点覆盖问题为例，我们应用该方案进行了验证。针对支配集问题，我们还证明Alber等人（JACM 2004）提出的经典核化算法可在多项式时间与O(k log n)空间内实现。在此过程中，我们开发了用于计算区域分解及近似上述问题的受限内存算法，这些算法可能具有独立的研究价值。