On the Parameterized Complexity of Computing Graph Bisections

  • René van Bevern
  • Andreas Emil Feldmann
  • Manuel Sorge
  • Ondřej Suchý
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8165)


The Bisection problem asks for a partition of the vertices of a graph into two equally sized sets, while minimizing the cut size. This is the number of edges connecting the two vertex sets. Bisection has been thoroughly studied in the past. However, only few results have been published that consider the parameterized complexity of this problem.

We show that Bisection is FPT w.r.t. the minimum cut size if there is an optimum bisection that cuts into a given constant number of connected components. Our algorithm applies to the more general Balanced Biseparator problem where vertices need to be removed instead of edges. We prove that this problem is W[1]-hard w.r.t. the minimum cut size and the number of cut out components.

For Bisection we further show that no polynomial-size kernels exist for the cut size parameter. In fact, we show this for all parameters that are polynomial in the input size and that do not increase when taking disjoint unions of graphs. We prove fixed-parameter tractability for the distance to constant cliquewidth if we are given the deletion set. This implies fixed-parameter algorithms for some well-studied parameters such as cluster vertex deletion number and feedback vertex set.


Vertex Cover Vertex Weight Problem Kernel Bisection Width Bisection Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • René van Bevern
    • 1
  • Andreas Emil Feldmann
    • 2
  • Manuel Sorge
    • 1
  • Ondřej Suchý
    • 3
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  2. 2.Combinatorics & OptimizationUniversity of WaterlooCanada
  3. 3.Faculty of Information TechnologyCzech Technical University in PragueCzech Republic

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