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In this talk we present an overview on the modern state of optimal geometrical graphs investigation. A special attention is paid to various generalizations of the famous Steiner problem. In particular, we discuss recent results in new branch of the area mentioned above, namely, in minimal fillings theory. The latter extremals appeared as a mixture of Gromov minimal fillings (more exactly, of their stratified variant) and Steiner minimal trees.

Minimal network, Steiner minimal tree, Steiner problem, Gromov minimal filling, one-dimensional minimal filling