The rectilinear Steiner arborescence problem is NP-complete

Given a set P of points in the first quadrant, a Rectilinear Steiner Arborescence (RSA) is a directed tree rooted at the origin, containing all points in P, 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 major open problem, and has important applications in VLSI. In this paper, we prove the problem is strongly NP-complete. The proof also shows the Euclidean version of the Steiner Arborescence problem is NP-hard.

• Type: Conference
• Year: 2000
• Where: SODA
• Authors: Weiping Shi, Chen Su
• Keywords: Algorithms, Major Open Problem, Rectilinear Steiner Arborescence, SODA 2000, Steiner Arborescence Problem