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This paper presents an approximation scheme for the Kantorovich–Rubinstein mass transshipment (KR) problem on compact spaces. A sequence of finite-dimensional linear programs, minimal cost network flow problems with bounds, are introduced and it is proven that the limit of the sequence of the optimal values of these problems is the optimal value of the KR problem. Numerical results are presented approximating the Kantorovich metric between distributions on [0, 1].

An approximation scheme for the Kantorovich–Rubinstein problem on compact spaces