## Steiner trees for terminals constrained to curves.(English)Zbl 0869.05023

Summary: We give a polynomial time algorithm for solving the Euclidean Steiner tree problem when the terminals are constrained to lie on a fixed finite set of disjoint finite-length compact simple smooth curves. The problem is known to be NP-hard in general. We also show it to be NP-hard if the terminals lie on two parallel infinite lines or on a bent line segment provided the bend has an angle of less than $$120^\circ$$.

### MSC:

 05C05 Trees 90B85 Continuous location 68R10 Graph theory (including graph drawing) in computer science
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