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Parameterized Problems on Coincidence Graphs

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Book cover Algorithms and Computation (ISAAC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4288))

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Abstract

A (k,r)-tuple is a word of length r on an alphabet of size k. A graph is (k,r)-representable if we can assign a (k,r)-tuple to each vertex such that two vertices are connected iff the associated tuples agree on some component. We study the complexity of several graph problems on (k,r)-representable graphs, as a function of the parameters k,r; the problems under study are Maximum Independent Set, Minimum Dominating Set and Maximum Clique. In this framework, there are two classes of interest: the graphs representable with tuples of logarithmic length (i.e. graphs (k,r)-representable with r = O(k logn)), and the graphs representable with tuples of polynomial length (i.e. graphs (k,r)-representable with r = poly(n)). In both cases, we show that the problems are computationally hard, though we obtain stronger hardness results in the second case. Our hardness results also allow us to derive optimality results for Multidimensional Matching and Disjoint r -Subsets.

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Author information

Authors and Affiliations

  1. LIRMM, 161 rue Ada, 34392 Cedex 5, Montpellier

    Sylvain Guillemot

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  1. Sylvain Guillemot
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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Japan

    Tetsuo Asano

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© 2006 Springer-Verlag Berlin Heidelberg

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Guillemot, S. (2006). Parameterized Problems on Coincidence Graphs. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_27

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  • DOI: https://doi.org/10.1007/11940128_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49694-6

  • Online ISBN: 978-3-540-49696-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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