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Bidimensionality and Parameterized Algorithms (Invited Talk)

Author Dimitrios M. Thilikos



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Dimitrios M. Thilikos

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Dimitrios M. Thilikos. Bidimensionality and Parameterized Algorithms (Invited Talk). In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 1-16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.IPEC.2015.1

Abstract

We provide an exposition of the main results of the theory of bidimensionality in parameterized algorithm design. This theory applies to graph problems that are bidimensional in the sense that i) their solution value is not increasing when we take minors or contractions of the input graph and ii) their solution value for the (triangulated) (k x k)-grid graph grows as a quadratic function of k. Under certain additional conditions, mainly of logical and combinatorial nature, such problems admit subexponential parameterized algorithms and linear kernels when their inputs are restricted to certain topologically defined graph classes. We provide all formal definitions and concepts in order to present these results in a rigorous way and in their latest update.
Keywords
  • Parameterized algorithms
  • Subexponential FPT-algorithms
  • Kernelization
  • Linear kenrels
  • Bidimensionality
  • Graph Minors

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