FPT-space Graph Kernelizations

07/22/2020

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by   Frank Kammer, et al.

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Let n be the size of a parametrized problem and k the parameter. We present polynomial-time kernelizations for Cluster Editing/Deletion, Path Contractions and Feedback Vertex Set that run with O(poly(k) log n) bits and compute a kernel of size polynomial in k. By first executing the new kernelizations and subsequently the best known polynomial-time kernelizations for the problem under consideration, we obtain the best known kernels in polynomial time with O(poly(k) log n) bits. Our kernelization for Feedback Vertex Set computes in a first step an approximated solution, which can be used to build a simple algorithm for undirected s-t-connectivity (USTCON) that runs in polynomial time and with O(poly(k) log n) bits.