抄録
Network synthesis problem is the problem of constructing a minimum cost network satisfying a given flow-requirement. A classical result of Gomory and Hu is that if the cost is uniform and the flow requirement is integer-valued, then there exists a half-integral optimal solution. They also gave a simple algorithm to find a half-integral optimal solution. In this paper, we show that this half-integrality and the Gomory-Hu algorithm can be extended to a class of fractional cut-covering problems defined by skew-supermodular functions. Application to approximation algorithm is also given.
