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Turing Kernelization for Finding Long Paths and Cycles in Restricted Graph Classes

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Algorithms - ESA 2014 (ESA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8737))

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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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Authors and Affiliations

  1. University of Bergen, Norway

    Bart M. P. Jansen

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  1. Bart M. P. Jansen
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Editors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, USA

    Andreas S. Schulz

  2. Karlsruhe Institute of Technology (KIT), Kaiserstruhe 12, 76131, Karlsruhe, Germany

    Dorothea Wagner

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44776-5

  • Online ISBN: 978-3-662-44777-2

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