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Abstract

In this paper, we unify several graph partitioning problems including multicut, multiway cut, and k-cut, into a single problem. The input to a requirement cut problem is an undirected edge-weighted graph G=(V,E), and g groups of vertices X 1, ⋯ ,X g  ⊆ V, each with a requirement r i between 0 and |X i |. The goal is to find a minimum cost set of edges whose removal separates each group X i into at least r i disconnected components.

We give an O(log n log (gR)) approximation algorithm for the requirement cut problem, where n is the total number of vertices, g is the number of groups, and R is the maximum requirement. We also show that the integrality gap of a natural LP relaxation for this problem is bounded by O(log n log (gR)). On trees, we obtain an improved guarantee of O(log (gR)). There is a natural Ω (log g) hardness of approximation for the requirement cut problem.

Keywords

Approximation Algorithm Greedy Algorithm Steiner Tree Residual Graph Graph Partitioning 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 2005

Authors and Affiliations

  • Viswanath Nagarajan
    • 1
  • Ramamoorthi Ravi
    • 1
  1. 1.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA

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