Minimum Manhattan network is NP-complete

@inproceedings{Chin2009MinimumMN,
  title={Minimum Manhattan network is NP-complete},
  author={Francis Y. L. Chin and Zeyu Guo and He Sun},
  booktitle={Symposium on Computational Geometry},
  year={2009}
}
A rectilinear path between two points p,q∈ R2 is a path connecting p and q with all its line segments horizontal or vertical segments. Furthermore, a Manhattan path between p and q is a rectilinear path with its length exactly dist(p,q):=|p.x-q.x|+|p.y-q.y|. Given a set T of n points in R2, a network G is said to be a Manhattan network on T, if for all p,q ∈ T there exists a Manhattan path between p and q with all its line segments in G. For the given point set T, the Minimum Manhattan Network… CONTINUE READING