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# 🌳 Steiner Tree

Band 9 — The Pluto transformer. Connect required points with the shortest possible network, optionally using intermediate points.

Terminals: 5
Ready

### Algorithm: MST-based Approximation

Compute the Minimum Spanning Tree over the complete graph of terminals. The MST provides a 2-approximation to the Steiner tree. For improved results, iteratively find Steiner points that reduce total edge length. O(k² log k) for k terminals.

### Why This Matters

Steiner Tree finds optimal networks — roads, circuits, pipelines. The Pluto transformer connects the dots with minimal total length, exactly how the 72-band framework connects frequency nodes.