Abstract
The minimum 3-way cut problem in an edge-weighted hypergraph is to find a partition of the vertices into 3 sets minimizing the total weight of hyperedges with at least two endpoints in two different sets. In this paper we present some structural properties for minimum 3-way cuts and design an O(dmn3) algorithm for the minimum 3-way cut problem in hypergraphs, where n and m are the numbers of vertices and edges respectively, and d is the sum of the degrees of all the vertices. Our algorithm is the first deterministic algorithm finding minimum 3-way cuts in hypergraphs.
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