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The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number

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Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

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Abstract

In the framework of parameterized complexity, exploring how one parameter affects the complexity of a different parameterized (or unparameterized problem) is of general interest. A well-developed example is the investigation of how the parameter treewidth influences the complexity of (other) graph problems. The reason why such investigations are of general interest is that real-world input distributions for computational problems often inherit structure from the natural computational processes that produce the problem instances (not necessarily in obvious, or well-understood ways). The max leaf number of a connected graph G is the maximum number of leaves in a spanning tree for G. Exploring questions analogous to the well-studied case of treewidth, we can ask: how hard is it to solve 3-Coloring or Hamilton Path or Minimum Dominating Set for graphs of bounded max leaf number? We do two things:

(1) We describe much improved FPT algorithms for a large number of graph problems, for input of bounded max leaf number, based on the polynomial-time extremal structure theory associated to the parameter max leaf number.

(2) The way that we obtain these concrete algorithmic results is general and systematic. We describe the approach.

This research has been supported by the Australian Research Council through the Australian Centre for Bioinformatics, by the University of Newcastle Parameterized Complexity Research Unit under the auspices of the Deputy Vice-Chancellor for Research, and by a Fellowship to the Durham University Institute for Advanced Studies. The authors also gratefully acknowledge the support and kind hospitality provided by a William Best Fellowship at Grey College while the paper was in preparation.

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Author information

Authors and Affiliations

  1. University of Newcastle, Callaghan NSW 2308, Australia

    Michael Fellows & Frances Rosamond

  2. Durham University, Institute of Advanced Study, Durham DH1 3RL, United Kingdom

    Michael Fellows

Authors
  1. Michael Fellows
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  2. Frances Rosamond
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Editor information

Editors and Affiliations

  1. Dept. of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Institue for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Benedikt Löwe

  3. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, University of Siena, 53100, Siena, Italy

    Andrea Sorbi

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Fellows, M., Rosamond, F. (2007). The Complexity Ecology of Parameters: An Illustration Using Bounded Max Leaf Number. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_28

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  • DOI: https://doi.org/10.1007/978-3-540-73001-9_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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