Theory of Computing Systems

, Volume 39, Issue 6, pp 929–939 | Cite as

Balanced Graph Partitioning

  • Konstantin AndreevEmail author
  • Harald RackeEmail author


We consider the problem of partitioning a graph into k components of roughly equal size while minimizing the capacity of the edges between different components of the cut. In particular we require that for a parameter ν ≥ 1, no component contains more than ν · n/k of the graph vertices.

For k = 2 and ν = 1 this problem is equivalent to the well-known Minimum Bisection problem for which an approximation algorithm with a polylogarithmic approximation guarantee has been presented in [FK]. For arbitrary k and ν ≥ 2 a bicriteria approximation ratio of O(log n) was obtained by Even et al. [ENRS1] using the spreading metrics technique.

We present a bicriteria approximation algorithm that for any constant ν > 1 runs in polynomial time and guarantees an approximation ratio of O(log1.5n) (for a precise statement of the main result see Theorem 6). For ν = 1 and k ≥ 3 we show that no polynomial time approximation algorithm can guarantee a finite approximation ratio unless P = NP.


Approximation Algorithm Approximation Ratio Approximation Factor Decomposition Tree Polynomial Time Approximation Algorithm 
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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Mathematics Department, Carnegie-Mellon UniversityPittsburgh, PA 15213USA
  2. 2.Computer Science Department, Carnegie-Mellon UniversityPittsburgh, PA 15213USA

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