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Given a set of terminals in 2D/3D, the network with the shortest total lengththat connects all terminals is a Steiner tree. On the other hand, with enoughbudget, every terminal can be connected to every other terminals via a straightedge, yielding a complete graph over all terminals. In this work, we study ageneralization of Steiner trees asking what happens in between these twoextremes. Focusing on three terminals with equal pairwise path weights, wecharacterize the full evolutionary pathway between the Steiner tree and thecomplete graph, which contains intriguing intermediate structures.

Budgeted Steiner Networks: Three Terminals with Equal Path Weights