The Uniform Orientation Steiner Tree Problem is NP-Hard

Abstract

Given a set of n points (known as terminals) and a set of λ ≥ 2 uniformly distributed (legal) orientations in the plane, the uniform orientation Steiner tree problem asks for a minimum-length network that interconnects the terminals with the restriction that the network is composed of line segments using legal orientations only. This problem is also known as the λ-geometry Steiner tree problem. We show that for any fixed λ > 2 the uniform orientation Steiner tree problem is NP-hard. In fact we prove a strictly stronger result, namely that the problem is NP-hard even when the terminals are restricted to lying on two parallel lines.

DOI: 10.1142/S0218195914500046

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Cite this paper

@article{Brazil2014TheUO, title={The Uniform Orientation Steiner Tree Problem is NP-Hard}, author={Marcus Brazil and Martin Zachariasen}, journal={Int. J. Comput. Geometry Appl.}, year={2014}, volume={24}, pages={87-106} }