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 interconnection 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 min. Previous algorithms could only solve 16- or 17-point point problems within the 30 min 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.

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