The rooted terminal-only Manhattan cost-radius spanning-tree decision problem is weakly NP-complete, and the balanced height partition achieves both cost and radius within factor 2 of the independent optima.
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Provably Good Prim-Dijkstra Revisited: New Theory and a Practical Algorithm for a Classical VLSI Routing Problem with LLMs
The rooted terminal-only Manhattan cost-radius spanning-tree decision problem is weakly NP-complete, and the balanced height partition achieves both cost and radius within factor 2 of the independent optima.