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International Colloquium on Automata, Languages, and Programming

ICALP 2007: Automata, Languages and Programming pp 15–27Cite as

Subexponential Parameterized Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4596))

Abstract

We present a series of techniques for the design of subexponential parameterized algorithms for graph problems. The design of such algorithms usually consists of two main steps: first find a branch- (or tree-) decomposition of the input graph whose width is bounded by a sublinear function of the parameter and, second, use this decomposition to solve the problem in time that is single exponential to this bound. The main tool for the first step is Bidimensionality Theory. Here we present the potential, but also the boundaries, of this theory. For the second step, we describe recent techniques, associating the analysis of sub-exponential algorithms to combinatorial bounds related to Catalan numbers. As a result, we have \(2^{O(\sqrt{k})}\cdot n^{O(1)}\) time algorithms for a wide variety of parameterized problems on graphs, where n is the size of the graph and k is the parameter.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, N-5020 Bergen, Norway

    Frederic Dorn & Fedor V. Fomin

  2. Department of Mathematics, National & Capodistrian University of Athens, Panepistimioupolis, GR-15784, Athens, Greece

    Dimitrios M. Thilikos

Authors
  1. Frederic Dorn
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  2. Fedor V. Fomin
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  3. Dimitrios M. Thilikos
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Editor information

Lars Arge Christian Cachin Tomasz Jurdziński Andrzej Tarlecki

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Dorn, F., Fomin, F.V., Thilikos, D.M. (2007). Subexponential Parameterized Algorithms. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_4

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  • DOI: https://doi.org/10.1007/978-3-540-73420-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73419-2

  • Online ISBN: 978-3-540-73420-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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