Computational complexity for uniform orientation Steiner tree problems
ACSC '13 Proceedings of the Thirty-Sixth Australasian Computer Science Conference - Volume 135
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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 $120^\circ$.