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Multi-parameter Analysis for Local Graph Partitioning Problems: Using Greediness for Parameterization

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Abstract

We study the parameterized complexity of a broad class of problems called “local graph partitioning problems” that includes the classical fixed cardinality problems as max \(k\)-vertex cover, \(k\)-densest subgraph, etc. By developing a technique that we call “greediness-for-parameterization”, we obtain fixed parameter algorithms with respect to a pair of parameters \(k\), the size of the solution (but not its value) and \(\varDelta \), the maximum degree of the input graph. In particular, greediness-for-parameterization improves asymptotic running times for these problems upon random separation (that is a special case of color coding) and is more intuitive and simple. Then, we show how these results can be easily extended for getting standard-parameterization results (i.e., with parameter the value of the optimal solution) for a well known local graph partitioning problem.

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Authors and Affiliations

  1. LAMSADE, CNRS UMR 7243, PSL Research University, Université Paris-Dauphine, Paris, France

    Édouard Bonnet, Vangelis Th. Paschos & Émeric Tourniaire

  2. UMR 7606, LIP6, Sorbonne Universités, UPMC Université Paris 06, 75005 , Paris, France

    Bruno Escoffier

  3. UMR 7606, LIP6, CNRS, 75005 , Paris, France

    Bruno Escoffier

  4. Institut Universitaire de France, Paris, France

    Vangelis Th. Paschos

Authors
  1. Édouard Bonnet
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  2. Bruno Escoffier
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  3. Vangelis Th. Paschos
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  4. Émeric Tourniaire
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Correspondence to Édouard Bonnet.

Additional information

Research supported by the French Agency for Research under the program TODO, ANR-09-EMER-010.

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Bonnet, É., Escoffier, B., Paschos, V.T. et al. Multi-parameter Analysis for Local Graph Partitioning Problems: Using Greediness for Parameterization. Algorithmica 71, 566–580 (2015). https://doi.org/10.1007/s00453-014-9920-6

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  • DOI: https://doi.org/10.1007/s00453-014-9920-6

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