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• W2893572497 abstract "Parameterized complexity allows us to analyze the time complexity of problems with respect to a natural parameter depending on the problem. Reoptimization looks for solutions or approximations for problem instances when given solutions to neighboring instances. We combine both techniques, in order to better classify the complexity of problems in the parameterized setting. Specifically, we see that some problems in the class of compositional problems, which do not have polynomial kernels under standard complexity-theoretic assumptions, do have polynomial kernels under the reoptimization model for some local modifications. We also observe that, for some other local modifications, these same problems do not have polynomial kernels unless NP⊆coNP/poly . We find examples of compositional problems, whose reoptimization versions do not have polynomial kernels under any of the considered local modifications. Finally, in another negative result, we prove that the reoptimization version of Connected Vertex Cover does not have a polynomial kernel unless Set Cover has a polynomial compression. In a different direction, looking at problems with polynomial kernels, we find that the reoptimization version of Vertex Cover has a polynomial kernel of size 2k+1 using crown decompositions only, which improves the size of the kernel achievable with this technique in the classic problem." @default.
• W2893572497 created "2018-10-05" @default.
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• W2893572497 creator A5062653045 @default.
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• W2893572497 date "2022-07-25" @default.
• W2893572497 modified "2023-10-14" @default.
• W2893572497 title "Reoptimization of parameterized problems" @default.
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• W2893572497 doi "https://doi.org/10.1007/s00236-022-00428-y" @default.
• W2893572497 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/36045930" @default.
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