Thirty-five-point rectilinear steiner minimal trees in a day

Given a set of terminals in the plane, a rectilinear Steiner minimal tree is a shortest intercon-nection among these terminals using only horizontal and vertical edges. We present an algorithm that constructs a rectilinear Steiner minimal tree for any input terminal set. On a workstation, problems involving 20 input terminals can be solved in a few seconds, and problems involving 30 input terminals can be solved, on average, in 30 minutes. Previous algorithms could only solve 16 or 17 point problems within the 30 minute time bound. Problems involving 35 points can be solved, on average, within a day. Our experiments were run on uniformly distributed data on an integer grid.