Rectilinear steiner trees: Efficient special‐case algorithms

Abstract A minimal rectilinear Steiner tree for a set A of points in the plane is a tree which interconnects A using horizontal and vertical lines of shortest possible total length. Such trees have potential application to wire layout for printed circuits. Unfortunately, at present no practical algorithm is known for constructing these trees in general. We present two algorithms, each requiring a number of operations proportional to only a low degree polynomial in the number of points to be interconnected, for the special cases in which all the points of A lie on a small number of parallel lines or on the boundary of a rectangle.