The rectilinear Steiner arborescence problem is NP-complete
Weiping Shi, Su Chen · 2000
Abstract. Given a set of points in the first quadrant, a rectilinear Steiner arborescence (RSA) is a directed tree rooted at the origin, containing all points, and composed solely of horizontal and vertical edges oriented from left to right, or from bottom to top. The complexity of finding an RSA with the minimum total edge length for general planar point sets has been a well-known open problem in algorithm design and VLSI routing. In this paper, we prove the problem is NP-complete in the strong sense. Key words. Steiner tree, computational complexity, NP-complete