Approximating the Minimum k-way Cut in a Graph via Minimum 3-way Cuts
For an edge weighted undirected graph G and an integer k ≥ 2, a k-way cut is a set of edges whose removal leaves G with at least k components. We propose a simple approximation algorithm to the minimum k-way cut problem. It computes a nearly optimal k-way cut by using a set of minimum 3-way cuts.We show that the performance ratio of our algorithm is 2−3/k for an odd k and 2−(3k−4)/(k 2 −k) for an even k. The running time is O(kmn 3 log(n 2/m)) where n and m are the numbers of vertices and edges respectively.
KeywordsParallel Computing System Minimum Weight Edge Edge Weight Function Simple Approximation Algorithm Apply Induction Hypothesis
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