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... Optimal networks appear as solutions of the fol lowing natural problem: How to connect a finite set of points in a metric space in an optimal way? We cover three most natural types of optimal connection: spanning trees (connection without additional road forks ), shortest trees and local ly shortest trees, and minimal fil lings. ... If this infimum attains at some set N , then each minimal spanning tree for this N is called a shortest tree or a Steiner minimal tree connecting M . ...

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