The Rectilinear Steiner Arborescence Problem Is NP-Complete Academic Article uri icon


  • 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. 2006 Society for Industrial and Applied Mathematics.

published proceedings

  • SIAM Journal on Computing

author list (cited authors)

  • Shi, W., & Su, C.

citation count

  • 45

complete list of authors

  • Shi, Weiping||Su, Chen

publication date

  • January 2005