Divide-and-Conquer Algorithms for Partitioning Hypergraphs and Submodular Systems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Finding minimum 3-way cuts in hypergraphs
Information Processing Letters
Computing minimum multiway cuts in hypergraphs from hypertree packings
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
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Given a positive integer k and an edge-weightedundirected graph G = (V,E;w),the minimum k -way cut problem is to find asubset of edges of minimum total weight whose removal separates thegraph into k connected components. This problem is anatural generalization of the classical minimum cutproblem and has been well-studied in the literature.A simple and natural method to solve the minimum k-waycut problem is the divide-and-conquer method: getting a minimumk-way cut by properly separating the graph into two smallgraphs and then finding minimum k'-way cut andk''-way cut respectively in the two small graphs, wherek' + k'' = k. In this paper, we presentthe first algorithm for the tight case of $k'=\lfloor k/2\rfloor$.Our algorithm runs in $O(n^{4k-\lg k})$ time and can enumerate allminimum k-way cuts, which improves all the previouslyknown divide-and-conquer algorithms for this problem.