Tight Approximation Ratio of a General Greedy Splitting Algorithm for the Minimum k-Way Cut Problem

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut is to iteratively increase the number of components of the graph by h - 1, where 2 h k, until the graph has k components. The approximation ratio of this algorithm is known for h 3 but is open for h 4. In this paper, we consider a general algorithm that successively increases the number of components of the graph by hi - 1, where 2 h1 h2

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Mingyu Xiao, Leizhen Cai, Andrew C. Yao
• Keywords: CORR 2008, Education, Minimum K-way, Minimum Total Weight, Simple Algorithm