An exact rectilinear Steiner tree algorithm

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 an 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.<<ETX>>

[1]  Andrew B. Kahng,et al.  A new class of iterative Steiner tree heuristics with good performance , 1992, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[2]  Pawel Winter,et al.  An algorithm for the steiner problem in the euclidean plane , 1985, Networks.

[3]  David S. Johnson,et al.  The Rectilinear Steiner Problem is NP-Complete , 1977 .

[4]  Bowen Alpern,et al.  Rectilinear Steiner Tree Minimization on a Workstation , 1992, Computational Support for Discrete Mathematics.

[5]  Denton E. Hewgill,et al.  Exact Computation of Steiner Minimal Trees in the Plane , 1986, Inf. Process. Lett..

[6]  Forbes D. Lewis,et al.  Optimum Steiner tree generation , 1992, [1992] Proceedings of the Second Great Lakes Symposium on VLSI.

[7]  David S. Johnson,et al.  The Rectilinear Steiner Tree Problem is NP Complete , 1977, SIAM Journal of Applied Mathematics.

[8]  F. Hwang.  On Steiner Minimal Trees with Rectilinear Distance , 1976 .