Journal ArticleDOI
Cost allocation for steiner trees
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A set of points, called consumers, and another point called central supplier, are located in a Euclidean plane and the cost of constructing a connection between two points is proportional to the distance between them.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.read more
Citations
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Journal ArticleDOI
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Proceedings ArticleDOI
Applications of approximation algorithms to cooperative games
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References
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Journal ArticleDOI
Steiner Minimal Trees
E. N. Gilbert,H. O. Pollak +1 more
TL;DR: A Steiner minimal tree for given points in the plane is a tree which interconnects these points using lines of shortest possible total length as mentioned in this paper, where the length of the shortest possible line is chosen.
Journal ArticleDOI
On the Problem of Steiner
TL;DR: The Steiner point of T as discussed by the authors is the unique vertex of a triangle whose interior does not overlap with the vertices of T, and it can be found by the following simple construction: let a12 be the third vertex of the equilateral triangle whose other two vertices are a1 and a2, and let C be the circle through a1, a2 a12; then p is the intersection of C and the straight segment a12a3.
Journal ArticleDOI
Cost allocation for a spanning tree
Armin Claus,Daniel J. Kleitman +1 more
TL;DR: The problem of allocating cost in a spanning tree network is considered and methods are suggested that are preferred given different emphases among the criteria for such a function.