An improved divide-and-conquer algorithm for finding all minimum k-way cuts

Abstract

Given a positive integer k and an edge-weighted undirected graph G∈=∈(V,E;w), 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. This problem is a natural generalization of the classical minimum cut problem and has been well-studied in the literature. A simple and natural method to solve the minimum k-way cut problem is the divide-and-conquer method: getting a minimum k-way cut by properly separating the graph into two small graphs and then finding minimum k'-way cut and k''-way cut respectively in the two small graphs, where k'∈+∈k''∈=∈k. In this paper, we present the first algorithm for the tight case of . Our algorithm runs in time and can enumerate all minimum k-way cuts, which improves all the previously known divide-and-conquer algorithms for this problem. © 2008 Springer Berlin Heidelberg.