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Algorithmica

, Volume 71, Issue 3, pp 566–580 | Cite as

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

  • Édouard BonnetEmail author
  • Bruno Escoffier
  • Vangelis Th. Paschos
  • Émeric Tourniaire
Article

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.

Keywords

Parameterized complexity FPT Greedy Branching  Local partitioning problems 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Édouard Bonnet
    • 1
    Email author
  • Bruno Escoffier
    • 2
    • 3
  • Vangelis Th. Paschos
    • 1
    • 4
  • Émeric Tourniaire
    • 1
  1. 1.LAMSADE, CNRS UMR 7243PSL Research University, Université Paris-DauphineParisFrance
  2. 2.UMR 7606, LIP6Sorbonne Universités, UPMC Université Paris 06ParisFrance
  3. 3.UMR 7606, LIP6CNRSParisFrance
  4. 4.Institut Universitaire de FranceParisFrance

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