Abstract
We analyze the potential for provably effective preprocessing for the problems of finding paths and cycles with at least k edges. Several years ago, the question was raised whether the existing superpolynomial kernelization lower bounds for k-Path and k-Cycle can be circumvented by relaxing the requirement that the preprocessing algorithm outputs a single instance. To this date, very few examples are known where the relaxation to Turing kernelization is fruitful. We provide a novel example by giving polynomial-size Turing kernels for k-Path and k-Cycle on planar graphs, graphs of maximum degree t, claw-free graphs, and K 3,t -minor-free graphs, for each constant t ≥ 3. The result for planar graphs solves an open problem posed by Lokshtanov. Our kernelization schemes are based on a new methodology called Decompose-Query-Reduce.
This work was supported by the European Research Council through Starting Grant 306992 “Parameterized Approximation”.
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Jansen, B.M.P. (2014). Turing Kernelization for Finding Long Paths and Cycles in Restricted Graph Classes. In: Schulz, A.S., Wagner, D. (eds) Algorithms - ESA 2014. ESA 2014. Lecture Notes in Computer Science, vol 8737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44777-2_48
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DOI: https://doi.org/10.1007/978-3-662-44777-2_48
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