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(\mathrm{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( \mathrm{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.
Let n be the size of a parametrized problem and k the parameter. We present a full kernel for Path Contraction and Cluster Editing/Deletion as well as a kernel for Feedback Vertex Set whose sizes are all polynomial in k, that are computable in polynomial time, and use O( (k) \log n) bits . 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( (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.
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polynomial-time kernelizations for
a full kernel for Path Contraction and
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, Path Contractions and
as well as a kernel for
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that run with O(\mathrm{poly
whose sizes are all polynomial in k, that are computable in polynomial time, and use O(
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and compute a kernel of size polynomial in k
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