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- W3018596675 abstract "We extend the notion of lossy kernelization, introduced by Lokshtanov et al. [STOC 2017], to approximate Turing kernelization. An $alpha$-approximate Turing kernel for a parameterized optimization problem is a polynomial-time algorithm that, when given access to an oracle that outputs $c$-approximate solutions in $O(1)$ time, obtains an $(alpha cdot c)$-approximate solution to the considered problem, using calls to the oracle of size at most $f(k)$ for some function $f$ that only depends on the parameter. Using this definition, we show that Independent Set parameterized by treewidth $ell$ has a $(1+varepsilon)$-approximate Turing kernel with $O(frac{ell^2}{varepsilon})$ vertices, answering an open question posed by Lokshtanov et al. [STOC 2017]. Furthermore, we give $(1+varepsilon)$-approximate Turing kernels for the following graph problems parameterized by treewidth: Vertex Cover, Edge Clique Cover, Edge-Disjoint Triangle Packing and Connected Vertex Cover. We generalize the result for Independent Set and Vertex Cover, by showing that all graph problems that we will call friendly admit $(1+varepsilon)$-approximate Turing kernels of polynomial size when parameterized by treewidth. We use this to obtain approximate Turing kernels for Vertex-Disjoint $H$-packing for connected graphs $H$, Clique Cover, Feedback Vertex Set and Edge Dominating Set." @default.
- W3018596675 created "2020-05-01" @default.
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- W3018596675 date "2020-04-27" @default.
- W3018596675 modified "2023-09-23" @default.
- W3018596675 title "Approximate Turing Kernelization for Problems Parameterized by Treewidth" @default.
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