Subexponential Parameterized Algorithms

  • Frederic Dorn
  • Fedor V. Fomin
  • Dimitrios M. Thilikos
Conference paper

DOI: 10.1007/978-3-540-73420-8_4

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4596)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Frederic Dorn
    • 1
  • Fedor V. Fomin
    • 1
  • Dimitrios M. Thilikos
    • 2
  1. 1.Department of Informatics, University of Bergen, N-5020 BergenNorway
  2. 2.Department of Mathematics, National & Capodistrian University of Athens, Panepistimioupolis, GR-15784, AthensGreece

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