Abstract
AbstractIn 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.KeywordsApproximation AlgorithmGreedy AlgorithmSteiner TreeResidual GraphGraph Partitioning ProblemThese 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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