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International Symposium on Parameterized and Exact Computation

IPEC 2011: Parameterized and Exact Computation pp 207–218Cite as

Tight Complexity Bounds for FPT Subgraph Problems Parameterized by Clique-Width

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7112))

Abstract

We give tight algorithmic lower and upper bounds for some double-parameterized subgraph problems when the clique-width of the input graph is one of the parameters. Let G be an arbitrary input graph on n vertices with clique-width at most w. We prove the following results.

  • The Dense (Sparse) k -Subgraph problem, which asks whether there exists an induced subgraph of G with k vertices and at least q edges (at most q edges, respectively), can be solved in time k O(w)·n, but it cannot be solved in time 2o(wlogk)·n O(1) unless the Exponential Time Hypothesis (ETH) fails.

  • The d -Regular Induced Subgraph problem, which asks whether there exists a d-regular induced subgraph of G, and the Minimum Subgraph of Minimum Degree at least d problem, which asks whether there exists a subgraph of G with k vertices and minimum degree at least d, can be solved in time d O(w)·n, but they cannot be solved in time 2o(wlogd)·n O(1) unless ETH fails.

This work is supported by EPSRC (EP/G043434/1 and F064551/1).

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Authors and Affiliations

  1. School of Engineering and Computing Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, UK

    Hajo Broersma, Petr A. Golovach & Viresh Patel

Authors
  1. Hajo Broersma
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  2. Petr A. Golovach
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  3. Viresh Patel
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Editors and Affiliations

  1. MTA SZTAKI, Lágymányosi u. 11, 1111, Budapest, Hungary

    Dániel Marx

  2. Lehrgebiet Theoretische Informatik, RWTH Aachen, Ahornstraße 55, 52056, Aachen, Germany

    Peter Rossmanith

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Broersma, H., Golovach, P.A., Patel, V. (2012). Tight Complexity Bounds for FPT Subgraph Problems Parameterized by Clique-Width. In: Marx, D., Rossmanith, P. (eds) Parameterized and Exact Computation. IPEC 2011. Lecture Notes in Computer Science, vol 7112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28050-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-28050-4_17

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