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Given a set S of vertices in a connected graph G, the classic Steiner tree problem asks for the minimum number of edges of a connected subgraph of G that contains S. We study this problem in the hypercube. Given a set S of vertices in the n-dimensional hypercube Q n , the Steiner cost of S, denoted by cost(S), is the minimum number of edges among all connected subgraphs of Q n that contain S. We obtain the following results on cost(S). Let be any given small, positive constant, and set k = |S|.doi:10.1137/100797473 fatcat:2nzaa2w4vnfqrijtgox46xgk3e