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Let G = \ N, E \ be an undirected graph having nodes N and edges E. We consider the problem of partitioning N into k disjoint subsets N₁, , Nₖ of given sizes m₁, , mₖ, respectively, in such a way that the number of edges in E that connect different subsets is minimal. We obtain a heuristic solution from the solution of a linear programming transportation problem.
Earl Barnes (1982) studied this question.