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Theory of Computing Systems

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

Balanced Graph Partitioning

  • Konstantin AndreevEmail author
  • Harald RackeEmail author
Article

Abstract

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.

Keywords

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