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
) algorithm for the minimum 3-way cut problem in hypergraphs, where
are the numbers of vertices and edges respectively, and
is the sum of the degrees of all the vertices. Our algorithm is the first deterministic algorithm finding minimum 3-way cuts in hypergraphs.