Cost allocation for steiner trees

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Abstract
A set of points, called consumers, and another point called central supplier, are located in a Euclidean plane. The cost of constructing a connection between two points is proportional to the distance between them. The minimum cost required for connecting all the consumers to the supplier is given by a minimal Steiner tree. An example is given in which for every allocation of the total cost of the tree to the consumers, a coalition of consumers exists, which is charged more than the cost required for connecting its members to the central supplier.

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